Is there a text that limits “greeting the mosque” to the first three rows of the mosque?

We do not know of any
basis for this view. The prayer for Tahiyyat al-masjid (greeting the mosque)
may be done in any place in the mosque, it does not have to be done only in
the first three rows in the mosque. 

The matter is open; wherever it is easy for the Muslim to pray in any part of the mosque, he may pray there. 

And Allaah knows best.