Thank you for using our forum. My name is***** am another expert on the forum, and I hope to assist you today.
If I understand your question correctly, you have a mobile phone application that allows you to make purchases using your phone when linked to your credit card.
Your mobile phone carrier has currently blocked your number from participating in this particular application.
You are asking whether or not they have a right to do so.
The phone company can limit the use of application and data over their network (the contract is written by them, expect it to favor them). Usually these types of services are blocked when the carrier believes that there is a high risk of fraud such that they can be held liable to either merchants, card carriers, banks, or their own customers, for false charges (for example, if the particular app that you are using is one that they do not believe to be secure).
Other reasons include customers that have filed disputes over charges (I am most certainly not implying that this applies to you, I am only giving you other reasons why carriers would use this contractual right) - for example, a customer rejects several charges made on their phone, later found out to be valid charges (or perhaps not proven to be valid, but the carrier believes them to be valid - so there is a high risk of fraud associated with that account), rather than risk having future fraudulent activities, the carrier will deactivate that particular account holder's access.
However, there should be a reason that they are blocking your particular device - contacting your phone service's customer service should let you know why this particular app or feature is not being permitted on your device.
If you are unable to reach a resolution by simply calling the customer service, try sending them a formal letter (via USPS and keep a copy). Written letters (or even emails) tend to get better responses than simply verbal communications over the phone.