OMF v2.x, the latest version of the extension, works with any desktop checkout extension that you have installed.
If you don't like the way your checkout extension looks on the mobile site, you can disable it by applying one of the compatibility patches that OMF comes with:
This will force OMF to use the default checkout process.
Previous versions of OMF
They use the default mobile-optimized checkout. If you're using OMF v1.x with a checkout extension, please, enable the necessary compatibility patch: