Tense difference

This question is another one in the formal English test in the public-school. Some parents of my students are now strongly asserting that their children's answer is correct. They primarily base their rationale on the native's opinion who is working at the private English academy. Here is the context.

<Dialogue> (target age: 16)

Woman("W" as a contracted form below) : Thanks for the present, uncle.

Man("M" as abbreviated below): Have you got it, Linda?

W: Yes.

M: Good. I was worried that the present wouldn't arrive in time.

W: Thank you for the present. I just love it.

<Summary-Linda's diary>

I got a call from Unle Jack. He wanted to ask if I got the present. I thanked him and told him I ( ) it.

<Direction> : Fill in the blank based on the dialogue.

<The intended answer> : LOVED

The tense issue is what brings a trouble now. What I want to make a point is that students strictly have to refer to the context itself. If "love" is used, it immediately calls for the out-of-the context knowledge. We do not know if Linda has still a feeling of loving toward the present let alone whether Linda here is existing or not. I just want some of my students' parents to understand that the context is completely contrived for the purpose of test.

However, they insist that "love" be considered an alternative answer. I feel that their main agrument just comes from the native's opinion. Here is the bottom line.

Considering the context(plus, this is a formal test setting where the answer is strictly controlled) , do you think that "love" makes the alternative answer? (I am sorry for this long posting)