More like good recall - which I have to admit, shocked myself! Especially because I am not a Harrold collector. (I have one tool in my collection - a very early adjustable with a 'HARROLDS' marking and the only real attraction for me is that I am fond of the early 'no possessive apostrophe necessary' era of tool-and-die making.

)
I never noticed that little mark,
Oh, that's definitely not on you. Chances are astronomically greater that it's
not on the other Harrold tools you have. I have seen that FORGED STEEL USA in a triangular depression or stamped (both used as Harrold "tells") on tools
without the little abbreviated <-H-> TM much more often than with it. In fact, the
only example I have ever seen is the one that I clipped for you to suggest that Harrold may have been the mfgr of your perfect handle style screwdriver, on pliers, belonging to
@LesserSon. He posted them on the Harrold thread several years ago. He also has one posted on that thread that is similar, but no arrow, just an H in the same spot.
When you look on the Harrold thread and/or the general Pliers thread you will see that they were notorious for using several different logos and markings and sometimes (maybe more often than not) none at all. They also used just HARROLD, HARROLD in a triangle, HARROLD in a circle, a singular big H, etc. Frankly, it's a little nutty how many different branding tics they apparently had, especially for a mfgr of their caliber. (It's probably telling that there is no Harrold page on the Alloy Artifacts website. Not even in the Other Mfgrs list/section, which gets very obscure.)
The use of a triangle (which is irrelevant to you for this case) and the little abbreviated <-H-> TM are both echoes or remnants of early marketing. Despite how commonly their pliers are found, and maybe their bars, too, that particular marking doesn't appear to have been made in great quantities.
If your perfect handle screwdriver is HARROLD, and right now it sure seems harder to argue that it's not with that marking, it would be in pretty rare company, and you might want to see if LS has some idea of when he thinks his pliers with the same marking was made, because they seem to share production era.