There indeed is a way. IF you look at the connector you can see the silver pins.
If you look very closely you will see a Flap holding the pin in, if you push it down carefully the little flap will push down releasing the pin.
After removing the pin, can restore the flap to the original position using a knife.
This is where the hard part starts, you will have to un-crimp the rear of the pin and reshape it to be re-crimped.
Or using a high temp solder, solder the wire to the pin and replace in the connector.
Or you can purchase another one
here
Housing and terminals 6 way
I believe I found some at
Jameco and on
Ebay
This should make your search so easy now.