There's no simple answer, but here's a simple answer: All speaker grills are different. Some are designed mostly for looks, while some are designed to be acoustically transparent. The best sounding grills are down no more than a dB or so at 15 kHz. Another issue is diffraction caused by bulky grill frames, and this is potentially a bigger problem.
To complicate things, some manufacturers voice their speakers for flatter response with the grills on, and if you remove them, treble frequencies could peel paint.
By the way, "The Big Lebowski" is possibly my favorite movie.
"STFU, Donny!!"
"Nice marmot..."
"Careful, man, there's a beverage here..."
"I'm not Lebowski...I'm the Dude, man..."
"Donny, you're entirely out of your element here..."