NYRA has a website where they log all of their equine injuries.
https://breakdown.gaming.ny.gov/
In my opinion, the NYRA tracks (Belmont, Saratoga & Aqueduct) care the most about this issue. These three tracks have the highest purses and the most vet scratches.
All tracks want to have full fields, that brings in the betting money. A track offering a $100 purse is not going to get as many potential starters as a track offering $100k purses. Therefore, the former isn't going to be as "picky" as the tracks offering higher purses.