larry8 makes some good points. I'll add a few thoughts.
First off, I'm a State certified Animal Damage Control Agent. I deal with squirrels & other animals daily.
Yes,, they can be destructive. However,, PEOPLE can be the ones to prevent such issues.
How?
If you hear noises in the attic or walls etc,, DO NOT PUT IT OFF,, call a professional if you even suspect it's an animal of any kind. Allowing them time to build a nest, establish a residence,, & especially have babies creates bigger problems.
Do NOT think it's as easy as "blocking a hole" to stop them. This just usually causes more damages.
Do NOT call the local "handyman" to "fix" it. 99.9% of them are NOT animal experts. They can cause problems TRYING to fix the issues.
Do NOT believe the wives tale of "moth balls, peppermint, coyote urine," or other repellents will fix the problem. And the ultrasonic devices,, don't work either.
Trapping only removes the current residents. They have relatives. The structure MUST be fixed to prevent additional access by these relatives.
And trapping & relocating may require a permit,, or relocation may be illegal. (Squirrels can be potential rabies vectors.)
Plus, taking the offending critters "to the woods" or "down by the creek" is trespassing in some form. Plus,, State & Federal property is off limits for releasing animals on. Potential felony there. On private property,, I always ask this question; "If I have a problem animal,, would you want it on YOUR property?"
Again,, call a professional. We deal with such issues daily. And a GOOD pro will not only evict the offending animals,, they will also repair the entire structure to prevent re-entry. Just because you find the main entry point,, there may be MANY other potential entry points they can use or enlarge to become a new entry point.
Lastly,, often,, it may not be gray squirrels,, we also have a LOT of flying squirrel complaint calls. Again,, calling a Pro will get good information.
Now,, many states do not have as strict of regulations as other states. In NC,, (where I am,) we have restrictions. Obey the laws. Learn them BEFORE dealing with any problem critters.