the grills

Leave on or off? I have a yellow lab.

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!)
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.
My dog doesn't go near my stuff either.

Unfortunately, kids and others milling about the house can be harder to train I've found.

Plus, accidents do happen......

I always leave all my grilles on.
The only time my grills are on is when either of my 2 grandsons come over. With my mission/cyrus 782's speakers I couldn't hear any differences with the grills on or off. But I now have Dynaudio's C1's. The soundstage disappears with the grills on and opens up dramatically with them off. Which ever sounds better to you and how important is protecting the drivers are to you.
Some designers factor grill into sound of loudspeaker some suggest removing for best sound. As far as protection most grills will not stop a lab or Child or from pushing in cone. But it does keep it out of site and with kids out of mind. With dogs as long as it doesn't have a smell they like you should be ok. My dogs love the smell of certain drivers they do not damage. But they approach to smell which means press moist noise against cone if you let them. And I don't. My cats where harder on my loudspeakers than any child or dog. Thus today no more cats.
I keep mine off.

I do have a Bernese Mountain Dog who chewed through my $5k Crystal Cable speaker cables...:)...and chewed up my Logitech 1000 universal remote... Still love her...
My cats used to use the exposed label edge of my stored records as a scratching post. The sleeves took a beating but the contents survived luckily.
I like to leave my grills off, I find they use too much gas when kept on. It only takes a minute or two to warm up, not like the stereo which takes 15 or 30 minutes.
I do leave the grills on the speakers, can't say I notice a difference with or without.
Oh, and we have a big black and white cat
I checked my George Foreman manual and is says a hot dog takes five minutes but nothing about a yellow lab? Did you mean a black lab? I know of a good Cajun catfish recipe...
If your or any speaker grills have frames, those would be a source of arbitrary reflection.
I don't think it will matter with Electras - on or off should sound equally good.