Hi Shannon,
Unfortunately, there is not a specific Advanced Filter in which you could only apply to those who used a discount code.
However, you could include certain data tags within the email content, such as the Orders Payments, which appears as a table displaying all detail of the specific order and payment.
An additional question I have is how exactly are your Sponsors providing the clients the discount codes? If they were providing an actual weblink, you could create a weblink with a specific Reference ID only for those who will be receiving the discount, and then set an Advanced Filter within the email to only be sent to those who meet the Reference ID criteria.
Please let me know if there is any additional information I should be aware of in order to assist you further, or if you have remaining questions on this.
Best,
Danni