Hello! Another thing you can do is not save the integration logs, and for that you can disable the activity monitoring for a module from the Operation tab of the module in ServiceCenter. These rules apply for the module that the name appears on the URL (/ModuleName/rest/...).
That disables all screen, extension, integrations, ..., from the module while still giving you the errors.
Not sure how is your architecture or what else you have on your module that you need activity monitoring, but you have an isolated module just for your integration it is probably a good solution.
Kind Regards