Huh, whut tea eyeball bags?

Yup. One of my dear old grandmother's home remedies.

She used it as an eyewash to reduce redness and her "tired eyes" feeling.

Tea is sterile because you boiled it. It is fairly neutral because it is just a water infusion, and the tea itself is mildly medicinal.
Because you have strained and filtered the water when you made the tea there are no big pieces of trees or stones to scratch your eyeball.
The tea from a teabag is even cleaner as far as chunks of rubbish go.
There is some antibiotic activity from the stuff in the tea but it is pretty mild, maybe more placebo than anything.
The little bit of tannic acid works to contract the small blood veins (capillaries) and makes redness go away.

So yes, Littlefoot, tea bags can be used to squeeze tea out of for eyewash after you drank most of the tea.
Just remember that you want your eyeball tea cold instead of hot so let it cool off to about body temperature before splashing it into your eyes.

Now for the big don't do this at home warning.
The tea is not for when you have any obvious damage to the eye. In that case the best you can do is to cover it and hope for a specialist to get to it.
(that is unless you are an eye specialist)

But tea is good as an eye rinse.