Pilot jet unscrewed but stuck in carburetor?

I'm rejetting my 2006 Honda Crf250x and I'm having trouble getting the Pilot jet out. It turns freely with a flat head screwdriver and if I tip the carb upside down it will fall partly out, but I can't get it to come all the way out even if I pull on it with a pair of tweezers. I can't take the float bowl off at the moment because the previous owners has mangled the heads of the screws. Does anyone know what the jet could be catching on or have any suggestions?

Get a dremel tool and a pack of fine abrasive blades. Use the dremel and blades to cut a line across the stripped heads that hold the float bowl on.
You can then use a slot head screwdriver to remove the float bowl.

Ask around, odds are someone you know has a dremel and all you'll have to buy is a pack of blades. Worst case, you can get a cheap, off brand at Harbor Freight for under 20 bucks.

I'm not certain that this is the case here but I have had a problem with a mangled o-ring doing something similar in the past, could even be a circle to prevent the jet falling out, looks like you will have to get the float bowl off first, you will need to do that anyway.

Drill the heads of the screws that holds the bowl. When you get the bowl off, wedge the pilot jet with a flat screwdriver while turning it with a pair of pliers. If you have the funds, just get a new carb. There are plenty of them on Ebay and Amazon.