Oh Brenda that is a pain. Do you happen to have a pair or surgical forceps (hemostat) as these could well remove that stubborn little piece of thread quite easily. These surgical forceps can come in a variety of sizes, a popular one is about 5" long and can come straight or curved, and look like a pair of scissors only they are not, they have a locking device on the handle so when you open the blades which are grooved inside, and then applied to whatever, and the handles shut and locked you get superb grip - they are brilliant.
If you haven't got any but think you would like some, ask in your local pharmacy if then can order some for you or alternatively if you go to a Chiropodist they might be prepared to order them for your, Roughly about £5.00.
These forceps are excellent for the overlocker as well. I have a tiny pair that my sister brought over from Canada, and the accompanying leaflet gave a long list of uses in the sewing and crafting world, and also useful in the First Aid box and for fishing - removing fish hooks from both fingers and fish.
Hope you get this sorted soon.