Hello, we have an application for creating orders and processing our customers loyalty cards by redeeming (removing) points from their account.
We are looking for a hardware solution where the customer can swipe their card on an MSR and print a receipt at transaction completion.
Is it possible to integrate the payment terminal in this manner?
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Based on the information you’ve provided, the following documentation will help answer your question:
Square Developer Documentation
Use a Gift Card (Custom Processing System)
Take a Payment
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Are these custom loyalty cards or are these credit cards baring major card brands? 
Hi Bryan - thanks for the reply. These are our own in-house rewards cards. It has a simple account number encoded on track two of the magnetic stripe. We are essentially looking for a way to get the account number from the swiped card back to our POS (http endpoint.)
Currently, the only customizable card that can swipe with our hardware our gift cards. However the swipe will only be read from the Square app. We don’t currently have an API that will read swipe data and send it to a backend. We’re constantly working to improve our features based on feedback like this, so I’ll be sure to share your request to the API product team.