This review actually tested the laser’s output and found it to be 2mW, which should be fine for pets if you’re not pointing it directly into their eyes (which I assume you wouldn’t).

My one concern is that green lasers are actually diode pumped solid state lasers which produce green light by frequency-doubling infrared, and some designs can actually emit much more infrared than green. I’m not sure if the author tested for infrared.

Edit: I asked the author about IR and they got 2.1mW@1064nm, with the caveat that the laser power meter may not be very precise at low power levels. That’s probably not dangerous.