Could Jetpack be Causing a 303 Error?

I’m trying to connect my site to a service with WordPress integration (Printful). The integration failed, and they told me that when then send requests to my site, they get a 303 error (I saw this, actually) which they attributed to some kind of rules about requests (requests containing urls, specifically) on the part of my host (eHost). They said the host has to fix it.

My host’s tech support gave me some completely ridiculous answers at first, then followed up with the suggestion that my Jetpack is somehow causing this problem. They want me to do a manual reinstall, but before I go through all that I want to figure out whether this is an equally uninformed answer. Is it possible that a Jetpack plugin is causing a 303 error when Printful tries to query my site?