Are there any crawl space experts out there?

We had a ductless heat pump installed on our house. The technician who put piping under the house told my wife that we need to put insulation under the wood flooring. For the last 20 years I thought that the floors were insulated. Perhaps we just more I thought. Anyway I took a look today and here’s what I saw.

Other than the insulation being ripped out of place by rodents (probably just trying to keep warm), it looks pretty good. No moisture, rot, termite or other insect problems.

It gets pretty chilly around here in the Winter and of course we don’t want to waste energy.

I plan on replacing the insulation myself.

Is there a way to keep rodents from damaging and dislodging the insulation in the future?

Any helpful suggestions are very welcome.