I've never heard of "Binding Prayers" either. When I looked up the exact phrase on Google, I got almost all Protestant websites. The first website that says that it is a Catholic website has this to say about "Binding Prayers":
Q. 1. What is a "Binding prayer?"
A. 1. The term "Binding prayer" does not find its origin in the Holy Catholic Church. It is a ridiculous new concept (to hook people with the latest fad) that really is a very old concept, just under a different name.
The practice of "Binding prayers" is associated with those who are involved in the Charismatic movement and who are attempting to perform exorcisms. A "Binding prayer" is an attempt to bind the devil. Any such attempt should be left to a priest (exorcist) who has the authority from his Bishop.
It is very dangerous for a layperson to attempt exorcisms.
Source: https://www.catholicdoors.com/faq/1000/qu1000.htm
This appears to be a Novus Ordo affiliated website, but there really weren't many websites that using this term that even claim to be Catholic. I find it very hard to believe that even the FSSP is actually recommending something like this.