1. There's Plenty of Room For Post Gremlins 2 Sequels
Problem: This is where my evil plot is revealed. Yes Hollywood, you've probably suspected it all along. Whilst trying to talk you out of a Gremlins reboot, I have pitched you a Gremlins Sequel! I'll save the maniacal laugh for when you cut your checks, and proceed to explain how this makes sense. Gremlins isn't a closed off mythology, if anything it lends itself to a Creature Feature/Anthology vibe. To reboot the series would be to disown its origins, and those were some pretty awesome origins.
If They HAVE To...: Plan A: You could easily make a film where Billy and Kate's kid pals around with Gizmo because Billy and Kate eventually disown him. Why would they disown him? If you've seen Gremlins 1 and 2, imagine if they had to do that at least twice more. (Which leaves room for games and books to bridge the gap.) In the end, they'll all reunite and triumph once more, but the point is there doesn't need to be a re-invention of the classic we all know and love. You can simply continue the story and keep building the world you set up so long ago, especially because Joe Dante could use the work. Plan B: You can go the anthology route, as anthologies are cool again, and hire top Horror/Comedy directors to make "The Three Rules Anthology". Each entry could focus on a different rule of Gremlins lore, and could vary from funny to creepy and everywhere in-between. You'd revitalize the brand, without having to retread water, AND you could save a fortune by scaling back the production. There's no shortage of original ideas that can be had in the Gremlins Universe, they just need to be explored. Instead of remaking a popular property, find a novel way to reinvent or continue it. If you don't have a good idea for a sequel, then chances are you shouldn't be playing with the toys you call a franchise. As Mr. Wing would say, "You are not ready." Once more, I turn to you What Culture Republic...what say you?