Hi Tom --
It is possible to change the settings of an installed LTI tool, but doing so requires admin or instructor privileges (depending on whether or not you're modifying an installation at the sub-account or course level). The relevant API calls are documented here:
External Tools - Canvas LMS REST API Documentation
It'll be a bit of work to find all of the existing installations, though; I expect that you'd need to loop through all of the courses and sub-accounts and call the list-external-tools call for each of them in order to find all of the places where your tool is installed.
--Colin
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