It looks a bit like a female spade connector, but it has a couple of "tails" at the back of the curled part that lock it into the ceramic block, and a ramp at the front that guides the burner's contacts into place.
The metal of the connector on the right has gotten charred and has disintegrated where the burner contacts it.
Can I just find a replacement connector, or do I need to get an entire receptacle replacement kit?