One of the rules of Rashi's commentary to the chumash, made famous by Nehama Leibowitz z"l, is that Rashi brings a second explanation to a verse only if he is not fully satisfied with his first explanation. While the second explanation may answer one problem it creates others and it is only the combination of the two that gives a satisfactory explanation of the verse at hand. When we see three, four or five explanations to a verse we can be certain that the verse is most ambiguous. Sometimes the difficulty posed by the text is understanding the text itself, sometimes contextual and sometimes philosophical. This may be by design[1] but the more we need to explain the less clear the subject material is. So when one is forced to give no less than seven explanations we know we are dealing with a most obscure text. Such is the case with the rather startling statement of Rabbi Chelbo that "converts are difficult for the Jewish people as a scab." (Kiddushin 70b)
This seemingly rather negative assessment of converts is difficult to understand. Over and over again the Torah commands that we demonstrate sensitivity to the convert, love him, not oppress him, not be harsh towards him. The command to be sensitive to the convert appears up to 36 times in the Torah more than any other mitzva[2]. More than Shabbat, kashrut or taharat hamispacha. Yet as Tosafot (Kiddushin 70b, s.v. kashim) explains it is precisely because we have to be so careful in our treatment of converts that they are difficult for us. The Torah sets very hard standards and "it is not possible that we don't bring them pain." Converts are difficult for us - because we do not live up to what is expected of us. This is a rather pessimistic, even if realistic, view challenging us to see Torah's strong stance as motivation for displaying greater sensitivity and bring greater happiness and joy to converts.  
Yet if there is little a convert can do regarding the responsibility of others towards him there is even less they can do regarding Tosafot's next explanation. In a view that may come as a surprise to many Tosafot quotes the rabbinic teaching that "we are in exile only in order to recruit converts." (Pesachim 87b) Our mission of converting others to Judaism requires we live amongst non-Jews - without personal contact it is hard to convince someone to convert. It is the fact that the Torah allows, and according to this view greatly encourages conversion that we are in exile[3]. No wonder converts are difficult for us. Yet as the Tosafists themselves point out this Gemara stands in contradiction to the "difficult" time we give converts before agreeing to accept them.
While there is little that an individual convert can do regarding the above explanations there is something they can do regarding the explanations given by Rashi. He explains Rabbi Chelbo's statement on a most practical level, that converts are not expert in how to observe the mitzvoth. Judaism has 613 mitzvot with each mitzva having hundreds if not thousands of details. Even if many mitzvot are no longer applicable there is so much to know in order to practice Judaism properly. Not having grown up in an observant home they lack the instinctive feel, knowledge and ability to practice Judaism that their religious counterparts have. It is inevitable that they will make mistakes irrespective of their good intentions. Furthermore those who become close to converts - something the Torah greatly desires - may mimic some of the ignorant practices of converts.
Fascinatingly Tosafot who quotes without comment this explanation of Rashi also quotes an opposite approach. Converts are highly motivated and excited about their new status and are going to be even more meticulous in their observance than many a Jew by birth. Converts are "like scabs" because they are so good, they make us look bad and help "remind G-d of our sins." This insightful explanation which many of us have witnessed with our own eyes (and if not by coverts then with ba'alei teshuva) is recorded in the name of Rav Avraham the convert. I do not know how many non-Jews converted to Judaism in the Middle Ages but it was very, very few. Considering the status of Judaism in medieval Christianity it took a special type of person to do so, and one should expect that a convert would put a "positive spin" on Rav Chelbo's statement.  
The Tosafists themselves prefer an explanation, which may have had great resonance in the past but no longer does for many of us. This is based on a teaching of Rabbi Chanina that "the Divine presence rests only on families of pure pedigree", something by definition lacking amongst converts. 
Perhaps we can add another explanation. A scab is formed when there in an injury, allowing the affected area to heal at which point the scab falls away. Converts serve as a method to heal the moral wounds and failings of the Jewish people. All too often we are incapable of seeing our faults, faults that are obvious to others. Converts add a most needed fresh perspective that we who inhabit the Jewish bubble often cannot see. They attach themselves to us allowing healing and renewal and then become part of the Jewish body leaving nary a trace.
However we interpret the teaching of Rabbi Chelbo or whether it even represents mainstream thought matters little. What matters most is that we display heightened sensitivity to those who seek to join our people. Such will allow us to avail ourselves of that which converts can teach us. This is a challenge that we have not fully met. Let us do better.  
[1] As discussed here the Torah is often purposely ambiguous encouraging multiple layers of meaning including contradictory ones. 
[2]  While the Torah's admonition to be sensitive to gerim because we were gerim in the land of Egypt in context refers to strangers by using the term ger the Torah also teaches the need for sensitivity to converts whom the Torah teaches are in many ways strangers.
[3] Perhaps this can help explain why our generation has merited Jewish sovereignty in our land. Whereas in previous generations the only way to influence others was through personal contact today one can meet face-to-face even if one is thousands of miles away. Mass media and social media allows the sphere of influence to greatly expand. We now can be a light to others from afar i.e. the land of Israel, and hence the need for exile is no longer.