This fee/visa/tax/fund has been around for at least 15 years. If you are not aware of it personally it is because your wife by having a US passport does not have to pay it (Turks with any sort of foreign residency/work visa/ dual nationality do not have to deal with this). Pre-1997 it was called the "mass housing fund", since 2001 or so it is called something insipid like the special fund.

Like so much in Turkish society the idea is to soak the rich as they dodge taxes at every turn, i.e. if you have enough money to travel, the thinking goes, you have another $50 or so to pay the government (this is on top of all other travel fees/taxes/facility charges).