Pull your vent trim back off and spray 3M 77 spray adhesive between the rat fur and refletix, let it set a couple of minutes then press the rat fur back in place. I saw a couple of spots of your rat fur 2" trim strips edges have come loose, just use a hot glue gun to reattach the trim strips. The 3M 77 adhesive is
sold at Wally World or Lowes for about $10 a can.
If you have stains on the rat fur I use a hand held steamer and brush it with a stiff nylon brush.
Eddie