Schools know that LoIs are nonbinding, no matter how much they might wish they were. If the roles were reversed, I don't think schools would hesitate to rip the carpet out from under your feet and go back on their legally nonbinding "word" if it benefited them. If Mayo can undo 364 acceptances with no repercussions, you can take back a single LoI.
The rest of this is conjecture on my part.
You risk pissing off the LoI school by attempting to bargain for financial aid. The biggest action they could take in retribution is rescind your acceptance, which still feels unlikely to me.
First, decide how you feel about your current position. School A is the one with the LoI/without financial aid, and school B is the one with a scholarship. As things are now, would you take school B with their scholarship over school A without one? If so, congratulations, you have all the power. Forget about the LoI, try to bargain for a scholarship, and the worst thing that can happen (and it seems unlikely to me) is they will rescind your acceptance and you will still go to school B.
If you would consider taking school A over school B even without a scholarship, then your analysis is going to be a little bit more subjective. You'll have to weigh the potential benefit of a scholarship at school A with the risk of losing your acceptance at school A.
There is also the doomsday possibility. I'm mentioning this not because it's something I'd ever worry about, but because it is technically possible. School A could somehow tell school B that you're being sneaky, and you could lose both of your acceptances. The only way this could realistically happen is if school A had the time and resources to pursue a vendetta, and also could identify your acceptances (they're not going to call every school in the country). I'm not sure if the April 30th PTE/CTE stuff lets schools actually see what your other acceptances are, or if it's just a number, so I'd figure that out and adjust your reasoning accordingly.