AR Bolt catch screw up

Magnet?

Drill a tiny hole from the opposite side?
Compressed air?

A vacuum cleaner with a handkerchief over a small tube held or taped to the vacuum hose in such a way as to not lose suction with the smaller tube. (or try it without the tube). The cloth is to make sure you catch the part instead of it being vacuumed up.

The more loose the weave is in the fabric, the more suction you will have.

Or, some SuperGlue (the tiniest amount) or five minute epoxy on the end of a toothpick which has the sharp end removed. Set the slightest amount of the glue onto the toothpick tip and stick it (literally) into the little hole to set up the glue between the toothpick and the detent part.

Bent paper clip or a packing hook?

Find a spring that is about the same size as the pin on the end of the detent. Like in a ball point pen. Trim the end of the spring so the finished windings are removed. Insert the spring over the pin by counter rotating it, the spring should expand allowing it to slip over the pin. Once the spring is in as far as it will go rotate it in the opposite direction while pulling gently. The spring should now contract slightly gripping the pin. I used this method before on a simular problem and it worked for me. Good luck.

Hold it over a thick pile carpet and shake it, the pin will fall right out and get lost in the carpet and you can replace it with a new one. Happens to me all the time.

Have you tried any of the other suggestions yet?
Try a strong magnet over the hole with the hole pointed down. Tap on the back side of the receiver opposite the hole with a plastic/wooden/leather mallet. If you're still worried about marring the receiver, put a wash cloth or piece of leather over the point of impact.

Put it in the freezer for several hours. Then tap with a non marring hammer to shake it loose

Cheers
Mac.

Do You have access to a lathe or do you know someone with one?? If You do I'll get back to you.

If you have access to a lathe try this.
The plunger measures around .152 dia. with a turned down pin on the end that measures .093 dia. Get a #12D common nail. That measures around .150 dia. Cut off the head and face the end square. Using a 3/32 (.0938) or a #41 (.096) drill a hole in the end of the nail about 3/16-1/4" deep. De-grease the inside of the hole if you used any oil to drill it. Using a toothpick carefully put a very small amount of Red Loc-Tite inside the hole in the nail and slip it down over the .093 dia. end of the plunger. Let the loc-tite cure over night. That should be enough to pull the plunger out. Remember not to use to much loc-tite, you don't want any to transfer into the hole where the plunger is.

exactly what detent pin is this ???? there are are only 4 the only one that works near the bolt would be the one for the buffer tube if its in upside down just put the tips of a small needle nose pliers unside the hollow base and open the pliers while pulling up get back to me let me know how it comes out

AR-15 detent pin

Soundtrackzz:

I am guessing it went in after you put some (a lot of) oil on it as I probably would too. I always over oil and after assembly use compressed air to blow off the excess........

Anyway.....to get back to the problem, try squirting some carburetor choke cleaner or aerosol brake cleaner in there and dry out the oil which may be have a tendency to hold the tiny catch pin "stuck" to the side of the cavity with oil.

Eliminate the oil and it may shake around a little easier?

Good luck,
Ed