Q:

Will EHIC (blue) card pay for eye check while I am abroad?

I've got an Austrian work contract, and I'm resident there from more than 1 year, but now I'm in Italy for work and I will have to stay here for some other time. 
My insurance company is the Austrian Health Insurance (TGKK).
If I do an eye exam can I ask them to pay?

A:

I don't know all the details but the general idea is that the EHIC only covers unplanned medical care that becomes necessary during the trip. So if you fall ill and have an accident and suddenly experience some vision problems, I think you could definitely get your eyes checked. But if you just want to use the occasion for some routine check because you speak the language and it's convenient, you would need prior authorisation from your insurer back in Austria. It's not necessarily that difficult to get, especially if that procedure is cheaper or quicker in Italy.
If you are a posted worker (staying abroad for work for several months at a time, not merely a few days) or a student, you can also be covered through the EHIC and the length of your stay does have an influence on what counts as “necessary”. For example, if you have a chronic condition that requires monitoring, then a routine check should be allowed too.
One additional issue in this case is that eye/vision care is organised very differently in different countries. I can imagine situations in which seeing an ophthalmologist could be necessary but if by “eye check” you mean a visit to an optometrist then I don't think that would usually be covered. 
Another principle is that you get coverage on a par with people who are insured/covered by the local statutory health system. It means the rules of the country you are in apply, not those of the country where your insurance is from. And if there is some copayment or cost-sharing system in the country you are visiting, you won't get reimbursed for the full cost of the procedure. So if Italians have to pay for eye checks themselves, you might or might not be able to get money back from your insurer in Austria later but your EHIC won't cover it.

