You need crimes to have a trial? Theoretically cops are supposed to have reasonable, articulable suspicion of specific crime before even detaining someone. You might be looking for something like congressional review, but most of the things that have been reported on Thomas for example, aren't chargeable under current law. If our politics wasn't so incredibly fucked right now, theoretically they would impeach, but that's just about the only mechanism for dealing with justices. Even then, that's edit: continent contingent mostly on logical inference of this line in the constitution:

The judges, both of the supreme and inferior courts, shall hold their offices during good behaviour

which assumes that "bad behavior" means they can be removed, which translates in modern society as "if there is political will crime is legal." See also: Donald Trump, who very obviously should have been removed several times over, is basically exactly what the framers had in mind when designing mechanisms around impeachment/removal/emoluments, etc. for bad actors, but republicans just didn't feel like it? And much like Trump, even if congress did investigate and find say, normie crimes like embezzlement or insider trading or something, we face the possibility that you end up with a Justice in prison still ruling in much the same way the Republican front-runner for president is very obviously a raping, treasonous, insurrectionist. Like, that's why those bad-actor clauses are there, but again, that requires a congress that can function (lol Republicans can't even get a house speaker) and actually have the will to do so. As it is, I'm guessing half of the country is probably just like they were with Trump evading taxes and thinks that Thomas taking advantage means he's "smart" and he's actively advancing a bunch of the fucked up shit they want, just like the rest of the corrupt, illegitimate court.