Here's the plan, zipped.

And now the second try:

Attached is an actual plan and the current entire query. We did make some changes based on some of the feedback, so you'll see it's different than the original.

I love all the input everyone, really - lots of information to digest here. I'll try and get that information (and the actual execution plan) asap.

My god, why didn't I...

There is an index for ServiceDate on that table, although that table has a ton of indexes on it. We're very likely trying to do too much here (indexes with...

It's all in that link: https://www.brentozar.com/pastetheplan/?id=SJF21m0lU

INSERT INTO @retTable
SELECT c.ClaimID, cd.ServiceCode, c.ServiceDate, cd.ServiceQty, c.CareProviderID, ISNULL(cd.DiagnosticCode, c.DiagnosticCode), c.SpecialtyCode AS Speciality, 
   sg.GroupCategory AS ServiceCodeGroupCategory, 0,...

Gah! Sorry, didn't mean to post twice - site timed out during the original post.