I don’t know. If it is glued on, I would guess there is a chance you will always be able to see where the glue was after removal. Or if there is any fading of the fabric, you might end up with a logo sized darker spot on the grill cloth. If it is a mechanical attachment, there will likely be visible evidence of the attachment mechanism.
If it is glued on, it may come off with the application of a little heat and prying. So long as you don’t overheat it, you should be able to give that a try without harm.