The second Mrs de Winter is, in many ways, a thankless part.

You have exactly defined the situation, and ours is by far the more disagreeable and thankless part to play.

Manfully he stuck to the thankless part he had to play, and admitted that ill-health had something to do with his strange behavior.

A lot of jobs are "thankless ." We only notice the thankless part with certain jobs where someone should be thanked, I guess.