Instead of deleting the existing hair group, it might be easier to create an new "No Hair" group, add the polys you don't want to be covered in hair, then exclude the No Hair group from the head and jaw groups. Once done, you can then delete that No Hair group.
For removing Eyes, Tongue, Teeth, Gums, Whiskers, etc., there are two ways you can approach it. If all polys on the entire head are covered in hair, you can Remove All, then Add / Material, and add just the FurEars and FurBody material zones. Or, you can take the longer route and Remove / Material, and then remove each of the material zones you don't want hair on. Unfortunately, it's not a multi-select (which would be great).
Remove Material works great too when you're painting the polys to add, and accidently include polys on the Tongue, Inner Mouth, etc.
View attachment 32665
I've used Remove Unseen to remove the inner polys too.