Screen time?

When do you allow your child "screen time"? Ever since my 4 month old started to become aware of his surroundings he strains to watch the tv or look at my phone while nursing, it can get very frustrating. Sometimes it's so bad and he's so distracted I'll have to go in another room and nurse in the dark in total isolation. I've read a few different things about babies having access to "screen time" but I'd like to hear from you guys.

He eats a ton, sometimes multiple times in 1 hour so nursing in a room by myself in silence can be a little bit daunting!