This type of connector is called a U.FL connector.
Replacing the connectors will be super fiddly, but is possible if you are skilled with a soldering iron. The cable side is the more difficult bit but also cheaper, so you might try a new antenna and replace just the PCB connector.
You may be able to use something small, like a pin, to carefully nudge the connector back into shape - it may make it worse, but if it doesn't work anyway what's to lose?!
Finally, you could unsolder the connector from the board, cut the wire and solder it directly. The wire will be a coaxial cable, so you need to take care not to short the inner to the outer - especially when soldering as you may melt the insulator away. The inner goes to the centre pin on the connector; the outer part to ground (the circle of the U.FL connector is connected to ground so you can use this pad).
Before you trust the receiver again you should do some range tests. You can put the transmitter in the range testing mode and check what kind of range you get.