You can force TeamCity to rebuild all dependencies if you add rebuildDependencies=true to query string:
http://testuser:testpassword@teamcity.jetbrains.com/httpAuth/action.html?add2Queue=bt10&rebuildDependencies=true
It is also possible to rebuild dependencies partially, but it is not easy as you'd need to retrieve some internal ids somehow but these ids aren't usually shown anywhere on the page.