I cant see why that housing over the catch bit didn't come loose when you removed the two screws holding it and with that removed the catch and a spring should drop out
slide hammer is what they use for removing certain dents. once you see one youll know how it works but the screws you get with them are usually soft so best to put a steel self tapper in it. screw it in thew top where the key goes and woosh! out she comes. slide hammers or dent pullers have been around for years and almost every car accessory shop sells them.