I remember using 外国人料金 or 追加料金. Not sure if there is a widely used standard expression for that.
The extra fee is usually split 50/50 between shop and princess. The regular fee 1/3 (shop) and 2/3 (girl). Sometimes it may be possible to negotiate on the fee if you choose a longer course. Once I had the princess herself make my reservation and still had to pay the extra fee. You can of course go to a place that doesn't charge a foreigner fee, but I usually pick my soaplands in advance, do some research on the girls, read their mobile phone diaries, scan the japanese blogosphere for reports, send a polite email in advance if foreigners are accepted etc. so if the shop charges an extra fee haggling or leaving is not really an option. They have me "by my balls".
Imho this is still an aftereffect of the AIDS-panic in the late 80s. Ogoto in Shiga prefecture banned foreigners completely in 1988 and it is still not easy to enter most of the teahouses. Almost all of the upperclass shops there have foreigners listed as no-go, among Yakuza, drunkards and minors.