How will test optional school decide who to give scholarships to?

I would absolutely still report your scores to test-optional schools unless it's exceptionally low. Getting merit-based scholarships at Ivies is extremely difficult (if not impossible, I don't know for every school, but many elite schools simply do not give out merit-based scholarships). That being said, the most competitive applicants for merit scholarships are those who are well above the average accepted student to that school. Because grade inflation (and deflation) is a thing at many schools, test scores an really help verify your academic preparedness on a more standardized level. While if you had exceptionally strong ECs you might still be in the running for merit scholarships at mid-range schools without test scores, lots of schools (Carthage, ASU, etc) actually award automatic aid based on GPA and test scores, and so not submitting your scores would effectively close off those sources as a possibility.

Unless you absolutely CANNOT take the ACT/SAT for some reason, or your scores are EXTREMELY low, I would submit test scores, especially if you're hoping for scholarships. Having an average/slightly low score at least proves that you're average/slightly below average and eliminates the possibility that you're not submitting scores because they're extremely low. If a school is test-optional and not test-blind, you are much better off submitting scores unless an exacerbating circumstance kept you from taking it, which you should explain to your schools. While they're not "required", standardized test scores CAN still impact your decision for admission and scholarships.

Hope that helps!

Little bit late to this, but you should know that Ivies (which it seems you're specifically asking about) do NOT offer merit based scholarships of any kind. Financial aid at Ivies is entirely need-based. So it will depend in its entirety on your family's household income and savings as communicated through the FAFSA and CSS Profile (the main financial aid applications).

Besides need some schools subsitute interveiws for test scores others will be based on essays and or GPA and or ECs.