The felt will sag and get limp just from being wet. The fact it is screwed up to the underside keeps it in shape.
If several screws are missing and it is wet, it will sag a lot.
It also can be washed rather easily.
So if it had oil on it, you can wash it off.
Then let it dry laying on the ground.
There are two 'tabs' under the car the felt sits on to toward the back. If those are not set in place in the felt, it sags even worse.
So I think your felt can be rescued, instead of replaced.
The screws are cheap enough.