Do not know what this is

[Tesumph]

What type of warm compress would work for her and how long should I hold it to her eye. She hates being held and not seeing anyone in the flock for (not joking) millisecond.

I understand, I’ve had some wild chickens.
Catch her in a beach towel and swaddle her like a baby so she can’t flap and scratch. Wet a washcloth with warm water and hold it on her eye for as long as the washcloth stays warm.
Maybe 10 minutes at a time, as many times a day as you and her can tolerate.