Not sure if it would do any good, but while it's still dry, I'd be tempted to run a vacuum with the smallest available nozzle over it while the latch is open. If you can get enough pressure then maybe it will pull some tiny bits of dust out of it, but probably not. Granted it's generally considered a no-no to use vacuums near motherboards because of ESD, but personally in this situation I'd do it anyway.

Other than that, it wouldn't hurt to put some alcohol in it, in the hopes that something will get washed elsewhere.
If you want to get more aggressive, maybe if you can find a thin needle or some other object that's small enough, you could dip it in alcohol, put it into the socket, add light pressure with the latch and then pull it out. Maybe it would do some good, but I've never tried it.

Consider reflowing solder joints in the surrounding area. This includes the pins of the socket if possible, but those would be tricky. The problem might not really be the socket contacts, but something nearby that's affected when you push on it.

Would have popped the moving part off the socket, begun with blowing it with pressurized air to remove any dust etc (vacuuming is dangerous, the air flow in the hose might cause electrostatic charge), then keept the socket soaked with some specialized electronics cleaning spray for an hour or so (isopropanol is too polar to be really effective on heavier greasy residues), rinsed the whole thing with the same product, blown it as dry as possible with pressurized air, and finally let the mobo sit for a day or so, to let any remaining electonics cleaning spray dry off. Make sure you get something without lubricating additives. In my opinion that's the best thing you can do, mechanical cleaning will take too much effort, and there's the risk of damaging the socket.