Q: How do I remove a tip of a headphone GLUED into my headphone jack ?

Maybe here:

Broken headphone jack! 3.5mm dillemma....: Apple Support Communities

If Apple can't remove it they will exchange your iPod for a refurbished one for this price. They do not fix yours.

Apple - iPod Repair price      

A third-party place like the following is less. Google for more.

iPhone Repair, Service & Parts: iPod Touch, iPad, MacBook Pro Screens

Replace the jack yourself if you are up to it

iPod Touch Repair – iFixit

I did finally remove the headphone jack just using APPLE IPHONE 4S/4/4G PHILLIPS CROSS HEAD MAGNETIC TIP SCREWDRIVER SCREW TOOL wich you can find on Ebay for $2.75. Just gently insert the screwdriver inside the remaining jack hole, turn clockwise and un-clokwise a copple of times, keep pulling and that´s it. No longer than 10 seconds!

Did they replaced are they said to replace the whole thing!!!!!!!

DId u fix it

Would this work on an iPad Air 2

It is not device specific. It is applicable to an iPod, iPhone and other devices with a 3.5 mm jack