I have the same problem actually, and i have a pretty new monitor. With old monitors, i simply spraied some bug-killer stuff on my monitor and they kept away, some of them went swimmin on it and stuff. These really piss me off, they leave those "dots" everywhere
Putting fruit juice or anything sweet near your computer won't deter them, it will only attract them. Just hang a light out of your window then the moths go there instead of in your window :}
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Anyways, maybe putting a tape on the monitor would help So some of the flies get stuck in there and other flies look "onoes, a trap!!!1" and problem solved?