I wouldn't do much of anything. Fungus gnats are more of a nuisance issue than a real concern for plant damage, especially wrt orchids or if a not very heavy infestation. I doubt I would risk repotting now, in the dead of winter and while the plant is in bloom.

I'd water the new orchids with the hydrogen peroxide mixture and keep the sticky traps in place. And allow the plants to dry a bit between waterings. The moss is a common potting media for phals in particular but it shouldn't be kept soaking wet. Allow to dry out some and expose the roots and media to the air for extra circulation (remove from decorative pot). That will help as well.

Or just treat with imidacloprid and be rid of them with one simple step. It won’t endanger the flowers as other treatments would.

I won't re-pot the plant now, it probably already got stressed out when a friend brought it to me while temps were around freezing point.

The very tightly packed moss is still very moist, so I have not watered the orchid yet with hydrogen peroxide. However I removed the plant from the plastic pot that had only one hole at the bottom, and temporarily stuck it in a wider vase so that all the surrounding area has more airflow. Surrounded with yellow traps, I keep it sort of isolated in the laundry room.

No imidacloprid or the likes here in Canada, sorry.

Do you have access to Mosquito Bits? It takes a few days and maybe multiple waterings (dissolve the mosquito bits in the watering can) but it works on fungus gnats!

In fact I already bought Mosquito Bits but haven't figured out yet how to use them.

If you had said you were in Canada I could have given country-appropriate advice. Sorry.

Imidacloprid is also banned in Europe for good reason. It's not something I'd want in my home.

Fungus gnats can be beaten by good watering practices.

Mosquito bits - sprinkle them on the soil surface before watering, or dissolve a capful in the watering can before watering. Whichever seems easier. You may need to repeat a few applications.

“Fungus gnats can be beaten by good watering practices.”

Hogwash.

I can show you many scientific papers on fungus gnat and shore fly control and none suggest that watering practices can eliminate them.

Phal orchids + wet moss = death.

The RHS recommends good watering practices as a method of fungus gnats control.

More myths from on high.

If it worked greenhouse growers everywhere would employ them. What they do in practice is a mix of cultural techniques and chemical control measures.

I get it, Tiffany that "Phal orchids + wet moss = death". But would "removing wet moss while blooming + repotting now" not also = death ? Which is worse ?

If wet moss equaled death the growers would not use it.

Relax. Enjoy the flowering cycle. When the flowers are done then repot into a medium that is good for your conditions.

“Imidacloprid is also banned in Europe for good reason. It's not something I'd want in my home.”

Do you treat your dogs and/or cats for fleas and ticks with a systemic?

I don't have either a dog or a cat. And if I did I wouldn't use these products. Pet flea treatments are poisoning rivers in the UK.

https://www.imperial.ac.uk/news/243875/toxic-flea-tick-treatments-polluting-uk/#:~:text=Imidacloprid%20and%20fipronil%20are%20powerful,those%20of%20mayfly%20and%20dragonfly.

https://sitem.herts.ac.uk/aeru/ppdb/en/Reports/397.htm

Furthermore, OP has a single orchid, not a commercial crop. Easy to deal with without chemical controls and cheap to replace if necessary.

Fungus gnats are weak fliers so even a ceiling fan in the same room will minimize their survival.

Thank you Orchid lovah for your concern and support. To protect my other 60+ plants I have been adding H2O2 every time when watering and placed yellow sticky traps. My 20+African Violets and other small plants only get water from the bottom, but I also have some huge plants too heavy for lifting, I can only water them from the top. Fungal gnats are almost gone but I still find the occasional one, often in the self watering AV pots. This week I will start with Mosquito bits. I need to be free of fungal gnats when I start my vegetables indoors from seeds.