What is the metal plate under the car above the exhaust pipe?

Is it a big repair if it's come loose on the back end? My mother's '07 Matrix has a metal plate underneath, starting not quite halfway back and slightly more on the passenger side just above what I believe is the exhaust pipe. It's held on by like 4 bolts on the front part and one further back. Or USED to be held by one further back, now it's flopping up & down and banging on that pipe.

The bolt is still in the the plate, running through a rubber-looking piece (some sort of gasket or shock absorber?), But not attached to the part that's attached to the car (a maybe 2" wide metal bar with a curved bottom running front to back, sticking out away from the actual bottom of the car). Very little of the bolt is sticking up out of the rubber piece to try to re-attach it. Is this a big fix (we're very short on funds)? Is it just a matter of replacing that bolt? Is there a nut on top of the bar it attaches to or does it just screw in? What is that whole thing called? Not sure I 100% trust the guy at the dealership,

He seemed to want a lot for what appears to my (very) untrained eye to not be too big a fix. Any guidence you could give me here would be most appreciated. She's getting out of the nursing/rehab home in a couple of weeks and we need to have her transport working.
I took a couple of pics