Before you get to using a screwdriver on it you might want to try a small pair of pliers or some strong tweezers.
We fit SD card connectors to our equipment at work and if the latching mechanism fails you can always slide the card out quite easily.
On the ones I've seen returned for repair the most common cause for failure is a foreign body inside the slot. Or a section of a cheap SD card has become detached and has wedged itself in there.
Getting any foreign object out might be difficult though.
Once the SD card is out you could get a can of compressed air (RS Components/Farnell) and use that to blow it out, if it's not wedged in too tight.
If that fails it'll have to be removed and taken apart