The implication of the 1099 is that this may be a *taxable* scholarship. The first thing to figure out, in connection with the business that issued it, is whether or not it is taxable.
Once you do that, yes the best way to handle it would be C-EZ, back it out, and if taxable it ends up on Line 21. Another way would simply be to put it on Line 21 to start with. Then use Tuition & Fees to zero out the taxable income, or the non-refundable portion of AOC to zero out tax. Or pay the tax and let parents take the full refundable credit if they qualify (and repay kid for tax paid).
This is a scenario where you really have to have both tax returns in front of you to figure the best overall results for the family as a whole. It would be foolishness to zero out a couple hundred bucks tax on the kid and have the parents lose $2,500 in credits.