Jim,I think this young lady got the kitten as an impulse,it can happen,more often than not.
They are incredibly cute easy to love,my Chico was an impulse-buy,turned out to be a good one however.
This little baby-kitten,needs so much more than this girl is prepared to give,so,yes IMO the kitten should be rehomed.
"The cruelest animal is the Human animal"
3 kitties,Rocky(r.i.p my boy),Chico,Vinnie