In music, a score is a musical document that contains parts of an orchestral performance. Credit means acknowledgement. So, this person has "scores of works to her credit" meaning it is acknowledged that she has many works done in her name. Credit also has another meaning. Credit is a type of currency built on trust. It is something that is used to obtain goods or services. When credit is used, there is credit debt that can only be paid off with money. So, I think this joke is tying in "credit score" which is a score that lets others know how responsible you are when it comes to paying off credit with "musical scores" and acknowledgement. This joke is playing on the words "credit" and "scores" and their different meanings. 
She ' s a composer who has scores of works to her credit .