It would be most helpful if you have a Collection Policy which states the type
of materials the museum collects.  If you don't have one, it might be
beneficial to develop one.  This can then be used to document the
appropriateness of this material to the museum collection.  If you need
assistance on writing a good Scope of Collection Statement (what we call our
official document), please let me know by replying back.  This document is
important even if you don't use it for this particular problem.  It will also
allow you to use it for the group of objects, not east individual one.  It
sounds like their letter shows some understanding of how most acquisitions
work - not acquiring duplicate objects for example.  I would also show that
you are able to care for the objects you are acquiring.

Once something is gifted, there should be no strings attached.  I don't
believe you would acquire something to just resale it, but you shouldn't be
prevented from any actions that a legal owner has.

Best of luck is what sounds like a difficult situation for a county historical
society which most likely has little to no staff to deal with such challenges.