"This is she" is the only correct answer. "Is" is a linking verb (to be form), and linking verbs are equivalent to "equal(s)". Thus This and she are equals, i.e., this=she. The answerer is saying "This is I". After the linking verbs "to be" is a predicate nominative - nominative form, not objective in this case.
“This is she” vs. “This is her”
"This is she" is the only correct answer. "Is" is a linking verb (to be form), and linking verbs are equivalent to "equal(s)". Thus This and she are equals, i.e., this=she. The answerer is saying "This is I". After the linking verbs "to be" is a predicate nominative - nominative form, not objective in this case.