Yes. They want you to include the claim number somewhere. I would also (or instead) put it on the form or letter.
They are asking you to give a reference. As a noun, here is a relevant definition.
- a. A note in a publication referring the reader to another passage or source.
The same dictionary shows some related definitions as a verb, and discusses a usage problem:
Usage Note: Though originally a noun, reference is often used as a transitive verb meaning "to supply (a book, article, or other work) with references." People also use the verb to mean "To cite as a reference" or simply "To mention or allude to." Though some traditionalists oppose these latter two uses of reference, the usage is most widely accepted when the context involves actual citing of sources. For instance, in our 2013 survey, fully 70 percent of the Usage Panel found The paper references several articles on global warming at least somewhat acceptable, while only 37 percent accepted the sentence During the press conference, the mayor referenced the recent floods.