Is there a regulation that points to not walking on the grass? Or states that all non hand receipt facilities are property of Drill SGT's?

Sir, don't try, you will just lose. Example- no Army Reg, to cover walking on grass- but we had a BN Cdr (LTC) issue an order to that effect in BN formation, Anyone caught walking on his grass received a Field grade ART 15, including some senior NCO's and 2nd/1st LTs. JAG said it was a lawful order and couldn't sway him. A normal career stopper for junior officers. He kept it up for 6months, until our mortars some how fired a walking barrage on a live fire in reverse. CID couldn't prove anything. DIV replaced him after his convalescent leave and no one ever remarked on the stick figures and jeeps white out on the base plates.

Command Policy, or simply the CSMs/1SGs lawful order. It is a reality that repeatedly walking on grass creates ugly/muddy paths eventually which ends up costing more time and resources to get them right in early spring to start over again.

There are two things in play, here. As far the grass goes, that's Government Property. As such, there is a requirement to treat it well. Walking on the grass can be tantamount to abuse of Government Property.

As far as whose property are all non-hand receipt facilities, that would be up to the unit commander. If said commander want that to be the DI, then so be it. That would be considered a verbal order.