Things I have used with varied success on moldy wood,
Bleach. The change is instant as the visible part of the mold body is killed and bleached. The benefit is often temporary with the mold coming back quickly. I think this is because the bulk of the mold organism is left intact and alive just under the surface.
Vinegar. The change from moldy to clean appearance is slower than bleach requiring some scrubbing. The return of the mold is also slower. The main benefit to you is it’s less harmful to you.
Alcohol. Rubbing or denatured, not scotch. Much the same as Vinegar.
Borax. The old fashioned soap. Inhibits future growth of mold. Wash, scrub the wood with Borax wipe it off, not quite completely leaving a light film, just let that dry.
I rented a home years ago that had a terrible mold problem in the wood window frames and sills. The full technique was:
Soak with bleach.
Scrub with vinegar and let dry.
Soak with alcohol and let dry.
A soaking wash with Borax, let it almost dry, gently wipe up any visible residue.
I didn’t just pull this process out of my back pocket. It is based on a piece I read decades ago on wood preservation by the navy on minesweeper hulls. I no longer have that print out so I’m working from memory. According to the author the navy used glycol and borate. The glycol soaks into the wood and desiccates the fungus body (dry rot stuff) and the borate keeps it from growing back. My thinking is that fungi and molds are similar enough that the wood rot treatment should work on mold as well. And that I don’t want glycol where I live. And that borax soap is readily available and contains a salt of boron.
Google the key words “wood preservative glycol borax” and you’ll get more links than you have time to read.
As for how did it work? Well, mostly, sort of. I had to repeat the process several times before I got the mold knocked back enough to relax. If it were my house I’d have removed the infected wood and replaced it much the same as planking destroyed by “dry rot” has to be replaced.
Here’s a link disucssing the effectiveness of borax on mold “
Does Borax Kill Mold”
If the mold on your teak vents is severe the best option may be to replace the vents.