How do I replace an AC return vent guard?

You can re finish the sheetrock and close the holes completely. Then screw back in. Another option would be to purchase a new cover that has a frame. Then you flip 2 levers to access the area.

You could place a small piece of tin foil into the holes and then reapply the screws which would help to tighten it up. The other option is to use wooden toothpicks and fill the hole with them, breaking them off so they are flat to the wall and the insert your screws. You could apply bit of glue to the toothpicks before inserting them and that would really make them sturdy.

So is this just screwed into the sheetrock? if so I would replace the screws and put plastic anchors in the drywall to secure the vent cover. If the drywall is ripped up, you could repair it first using joint compound, and then drill a hole the diameter of the anchor. Then tap the anchor in with a hammer. Then make sure your screws are just a bit fatter than the diameter of the anchor and a bit longer (this will force the anchor to spread and secure it in the drywall.

These vents come in a variety of sizes. Using a stud finder locate the studs on either side of the opening. They should be right where the opening begins on either side. Get a new grill that has holes in the same location as the studs. Studs in houses are almost always 16” apart. Install the new vent/grill securing it to the studs. Make sure the screws are long enough to go into the stud at least 1”. Remember to figure in the thickness of the drywall which is normally 1/2”, although 5/8” thick drywall is sometimes used. Use either deck or drywall screws. They have a very strong hold and are much less likely to strip out. If you can’t find screws that are the same color as the vent you can just paint the head whatever color you need. https://www.amazon.com/s?k=a%2Fc+air+return+grill&crid=3OMHNU22SHYO9&sprefix=A%2Fc+air+ret%2Caps%2C172&ref=nb_sb_ss_i_1_11