ENVI_FILE_MNG appears to work for me (file removed from the ABL) with the /remove keyword. Since you are working with Landsat, it may be that you have not accessed the correct FID for removal if it is not removed from the ABL. When you open Landsat, you get several FIDs due to the way it is stored as a meta-file (separate TIFFs with a metadata file associating the various files). Perhaps you have not passed the correct FID to remove the file. Also, if you are trying to remove multiple FIDs, then you would need to loop through each FID to remove it.

Assuming you're opening and closing files in a loop, you might try getting a list of all open FID's with envi_get_file_ids() at the beginning of the loop. Then at the end of the loop, get a new list of FID's via another call to envi_get_file_ids(), then close any FID's that were in the new list but not in the old one.