She contacts the person who contacted her (from the offer letter).
Yes. It is a careful dance. She first has to decide her hierarchy of schools, and what is most important to her (how much she wants the school vs the overall $$). Then she writes a very short/extremely polite email along the lines of "I was delighted to get the offer of a place and (whatever they called the scholarship). I am evaluating my options and wanted to confirm (deal). (Deal) can be what they offered, (“that this is the best offer you can make”) or it can be specific ("if you could match the offer that I have from X school, which is Y). It is important to be realistic, and honest with both herself and the schools. There is not going to be a bidding war- these programs are expected to make money for the school! and none of those schools are short of talented applicants.