I'll be glad to check your answer.
Check Rule 4 in this site.
http://grammar.ccc.commnet.edu/grammar/sv_agr.htm
17. Identify the choice that correctly completes the sentence:
Neither Kurt nor Sue has turned in _______ permission form.
their
his or her
his
they're
4 answers
It's a...?
No.
Really it's not a? Why not? I would go with b if not using their.