The outside scholarship giver can write the scholarship amount as “$X, or the amount that the student can receive in outside scholarships without having other grant and/or scholarship aid reduced, whichever is lower” and require the student to contact the college’s financial aid office to find out what the latter is and report back to the outside scholarship giver.
If more outside scholarships did something like this, then that could help put some pressure on colleges to apply outside scholarships first to unmet need, student loans, and expected student work earnings before reducing grants, since students with such outside scholarships may be financially influenced to choose colleges where their outside scholarships actually help them.