Hi Matthew, so I am no expert, but judging from the pictures you sent it does not seem like the receiver was damaged and could still be funtional. My suggestion would be to gently wigle the reciver left and right while pulling it out of the laptop. Then look and see what the correct orintion is for the black casing of the reciver would be. After that apply a small amount of super glue to the inside of the casing (not so small that it does not stick, but also not so much that super glue will ooze out of the casing). Lastly, put the casing back on the reciver in its correct orintion. I hope your mouse works and best of luck to you!
I say use superglue since for me it is easier to control how much glue I want to use, and I find that it works well in terms of strength for plastic.