how to prevent 3rd party from rendering mobile version of their site

I am currently using a 3rd party to process payments for my website. As part of the payment workflow, I have to redirect users to their site with some parameters (i.e. I do not have the option of not going to their hosted site).

The workflow works great on the desktop, however, when viewed on a mobile device, their site renders the mobile version, which is different from the desktop version and excludes an important option for our users.

They have said that they will not be updating the mobile version for some time, so I would like to know if there is a way to ensure that the desktop site is rendered even when accessed by a mobile device.

Any help would be much appreciated!