the grills

I leave them on, but then again, the grills on my Eggleston Works Andra II are very, very thin, and do not obstruct the sound. (And I much prefer the looks with them on.)

Most speakers do sound better with the grills off, but again, that depends on the type of speaker.

And we have a Bichon Frise, white of course.
And when I say "we", I mean my wife and daughter have one.
(And so why are we telling each other what type of dog we have?
They are not stinking cats, that use grills for scratching posts!)
;-)

I only mention the yellow lab because he sheds.

It depends on the speaker design.

For best sound, listen both ways and decide which you like better.

Grills help protect often delicate drivers. If you have delicate drivers,like soft dome tweeters say, and kids or pets or house cleaners or such running about, I'd leave them on and do something else relatively cheap and easy to tweak the sound if really necessary, like tweaking placement, toeing in/out, interconnects, even (gasp) tone controls if available etc.