The 3rd party fee you see listed on your Square report is what is known as an Application Fee.
The Application Fee you see listed on an invoice is part of how Square’s fees are allocated through their integration technology (which is used for the MassageBook’s Square integration). Typically, Square charges a higher rate for transactions run through the integration, and a portion of this higher fee is allocated back to the integration partner as part of the terms negotiated with Square when the partnership is formed.
This portion that the integration partner receives as part of the partnership terms is referred to as the Application Fee. However, in our specific case, we forgo the Application fee (i.e. Square keeps it), so that our users are not charged Square’s higher integration rate, but instead charged Square’s normal fees as advertised on their site. See this link for Square's fee schedule: Square's Fees
In other words, the Application Fee is not an additional fee but rather part of Square’s normal fee, just listed on a separate line item. If you total up the two line items for fees, you will see that they equate to Square’s normal processing fees of 2.6% + .10 or 3.5% + .15. Unfortunately, we do not have any control over the verbiage used to describe the fee or placement of that fee on the invoice.