How you handle disposing of the one and only “asset” from a relative’s “estate” is an issue you must decide on your own.
The most accurate answer to your question would be to open a probate estate for your grandmother and administer the assets of the estate through the court, as required by state law.
But if this check is the only asset that exists in the “estate”, cashing said check would be the end of that “estate” — assuming your bank will cash a check that does not have your name on it specifically. (Your question did indicate the check was made out to ‘the estate’ of your grandmother with your address below.)
So past these two statements, we cannot advise you on a further course of action.
For advice specific to any personal legal questions, Standard Legal always recommends you consult a qualified, licensed attorney; you can find a local attorney for FREE at Standard Legal’s Attorney Find page.