This is pretty hilarious. It's drafting tape with soldermask applied over it. You can tell from the width, color, and the texture (drafting tape has a pretty unique ripply-rough texture). This stuff:
It's pretty much standard to use this stuff for last minute bodges and various other "sticking-things-to-stuff" and "touching-up-the-mask" related activities at a PCB fab house. Especially on these phenolic paper single sided boards that are used throughout ultra-commoditized products like power supplies. They're pretty close to the platonic ideal of a 'crappy PCB.' Quality you can stomach at prices you'll lower your standards for!
I've taken apart many an old power brick or ATX power supply in my day (don't ask - I was a teenage male and wanted those 400V caps for...stuff) and occasionally you'll find weird things like this. Obvious mask touching up in the form of blocky copper artifacts in spots (like someone just taped over part before the photo resist was exposed), component and footprint mismatches, silkscreen that is simply wrong, and sometimes surprise 'leftovers' entombed under solder mask. Also, sometimes if you desolder some components, you'll catch a waft of foreign food smell. Seriously. I try not to think too hard about what is even going on with that one.
Who knows what happened, but there was something taped to it, or being touched up or fixed, or both and it may or may not have been intentionally left there. It looks like it was deliberately placed between the pin header pads, its usual use case involves small cuts and an exacto-knife. I suspect someone just forgot to remove it before the solder mask got applied and there it has stayed. The parts of the tape that were not covered (pin header connector pads) would have been scrubbed off during the cleaning and pre-HASL phase of the board manufacture, except for the bits safely shielded by the solder mask.
If there are these same strips on others of this board, then it was probably something that had to be touched up and some poor soul probably tapped strips of drafters tape on thousands of those boards. Maybe there was a problem batch, or even board, and it's not common to this whole run. Who knows. Either way, it doesn't really matter. There is no deeper engineering reason behind it, hence the inconsistent use of the tape. It is not involved in the circuit itself, but rather an artifact of the board's manufacture.
If you like, you can scrape off some solder mask and peel off a strip. It won't hurt anything if you pick some that is not covering copper, and you can empirically confirm this answer. And I'll update this answer and leave in shame if it turns out not to be good ol' drafting tape, but I am very certain that's exactly what is.
