I'm not too familiar with the format, but it sould like this might be something you can script and run from the command line with mapinfo? ( https://help.precisely.com/r/n/MapBasic/pub/2023/en-US/MapInfo-MapBasic-Reference/Pack-Table-statement ). If you could get a script running then you could 100% use FME to trigger it.
The other option which seems silly but may work is just reading the whole file with fme and writing it out a new one. From what I've read this would be equivalent to a packed file. I'm not sure if you can preserve 100% of the information from MapInfo though with FME so that would be something to check.
There is no MapInfo installed upon the Server where MapInfo is installed. In my organisation, MapInfo is only installed upon user’s PCs. So I cannot trigger a mapbasic script. I have considered doing the “output elsewhere and copy back” option, but it seems like a really clumsy work-around