Are they 'house flies' or those very small ones?
I had lots of the small ones last year, which I put down to something in a bag of house plant compost, as they only appeared after using that. They were a pain, but I didn't notice them on my TV (it was a CRT at the time).
If they're attracted to fruit (mine didn't seem to be) then maybe you could put a bowl of ripe, or even rotting, fruit in a corner and hope they find that more appealing than your screen!
Otherwise, this site may be helpful.
(I have two African Grey parrots, but they seem totally disinterested in eating flies - can't say I blame them, although I did swallow a large bluebottle about 10 years ago - I was cycling down a steep road, singing (!), and accidentally ate it - the taste is best described as extremely bitter 
)
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