Lay your sandwich out on a table; fold both the top and the backing back away from the damaged batting.
Trim away the damaged batting in a long strip.
Cut a new batting strip the width needed.
Butt the edges of the old batting and the new strip and use batting tape or a serpentine or zigzag machine stitch to join them (my preference).
Reassemble the sandwich and keep on keeping on!
But, I must say, it seems to me you have more problems than a torn batting if a mouse in your house has done such damage in one day. I hope you catch it....and all it's buddies.....quickly. Rodent droppings can be very hazardous to your health.
Jan in VA