You did say Stronghold? There are 4 holes in the adapter. Two are thru holes, two are threaded. Remove the two screws from the thru holes. (that's where they are now) and put them in the threaded holes. Now, and only now, slowly tighten up the two screws, evenly, and watch the insert rise out of the chuck. Cool, huh?
Now, be sure to clean out the recess really good with a solvent. Do not wax or oil the new insert and reverse the process with the screws in the thru holes.
Now, if you've tried this and it hasn't moved, remove the screws completely, put the chuck in your headstock and, while rotating by hand, tap on the chuck with a wood mallet. This will cause it to move out of the insert, which is slightly tapered. DO NOT TURN ON YOUR LATHE, This is what they really call a fatal error. Never apply heat, but you can try cold.
Hope you're successful.
BTW, it will take less time to change than it did to read this.