"Quite a number of the 767-331s have been parked..."
Of course you meant...767-323's when referring to AA delivered a/c.
-[x]31's would, of course, be indicative of an a/c built specifically for TWA.
That being said, I do not believe there ever was an a/c designated as a 767-3
31. TWA was an early customer for the 767-200 and a/c were built specifically for TWA and designated 767-231's . N601TW (L/N 14) - 610TW were -231's. N650TW and N651TW were -205's built for Braathens.
Records indicate that none of the P&W Powered (AA's are GE) 767-300s acquired from TWA by AA were built specifically for T-way.
The TWA 767-300 fleet at various times consisted of at least the following a/c...
24952 357 767-3Y0(ER) EI-CAL
24953 405 767-3Y0(ER) EI-CAM
25137 377 767-330(ER) N691LF
25403 409 767-33A(ER) N637TW
25411 408 767-3Y0(ER) N640TW
26205 474 767-3Y0(ER) N638TW
26208 505 767-3Y0(ER) N639TW
28132 692 767-3Q8(ER) N634TW
28207 695 767-3Q8(ER) N635TW
30301 762 767-3Q8(ER) N636TW
...which leads one to the assumption that they were originally built for GPA, Condor (LH), AWAS, and ILFC respectively if the -designations are correct.
The -200's were disposed of at or before the merge and did not operate as AA a/c.
The -300's which were acquired by AA were disposed of by December of 2001. Some are now stored, some scrapped, but many are still actively operated somewhere in the world.