The API for site management is declarative, not imperative. You do not explicitly add a site to or delete a site from a browser test. Instead, you update the test’s site collection. If the update message omits in its MonitorSite collection sites where the test is currently running, the test will no longer run on the omitted sites after the update.
The UpdateTests method of update requires you to first get an up-to-date snapshot of the test by calling GetTests(), filtering if possible its output by MonitorId. The Monitor element returned by this query contains a site collection which can be reduced on the update.
The UpdateTestParameters() method enables you to perform site management on a browser test without getting a snapshot of the test from the system and without traversing any code paths not related to site management.