I places a test logo in the style editor and tested the link and the logo appeared. I have since changed the logo and when I test the link the old logo remains and is not updated.
It is not clear in your posting, but I am assuming that you changed a style template and then applied those changes to a survey. Our first step in this type of problem would be to clear our caches.
SurvetGizmo has a function for clearing its link caches. You can get details at https://help.surveygizmo.com/help/clear-link-caches.
It is also possible that your browser is showing you a cached version of the survey. You can either refresh your view or clear your browser cache (https://help.surveygizmo.com/help/clear-cache-and-cookies).
If this does not help it would be useful to know the exact sequence of the changes you made and in what section of SurveyGizmo they were made.