In you do a GET or HEAD request and the server returns 307 you will get a response from the new location and there will be no error. For other verbs (such as PUT) you get an error, for safety reasons: by default the app does not redirect your (possibliy sensitive) input to other servers like that.
There are two possible solutions:
It looks like the external server is telling Mendix to use an alternative URL via a 307 redirect, but Mendix doesn’t know how to handle this.
One solution could be to turn on the REST Consume LogNode up to TRACE and see what the full response is from the server. It should give you an alternative URL to use, so try substituting this URL for the one you are using currently. This should only really be used as a temporary fix, but it may help in the short term.