So the scenario is the build failed and you now want to submit the work to the build again, but you decided the work itself does not need to change. So it is good to submit it again, maybe the build failed due to a server error for example, or a merge conflict in the schema or other file.
Use Team Explorer to select the BC Website Team Project, then the Builds section. The gated build is BC_Website CI, right-click on this and click Queue New Build...
The below window will then be displayed, you need to pick the shelve-set that contains your work, this will start with Gated at which is system generated name when you check-in. Then tick the box underneath that says you want the changed to be checked-in if the build works.
Finally click Queue.
Hopefully you'll find this a bit quicker than unshelving and re-submitting your work again.