I know this was asked a long time ago, but I run into this problem all the time every time and again, and I always forget how to do it, so I decided that I would post my solution, which, I think, might be a little easier ( depending on how you look at it).
Basically, I launched the TeamCity build, which, unfortunately, created a duff version of a third-party package that I tried to recreate, but with a few modifications. This did not work, but it meant that I was always provided with this duff package in the package manager, and it will remain so until a third party releases a newer version. So I wanted to remove the package from the TeamCity Nuget server, and the only way I could find it was to remove the assembly, which would also remove the artifacts (Duff Nuget package in this case).
Now I could not see a way to remove the assembly, except using the REST API, so I used it (I hope I'm not stupid, and in fact this is an easy way to remove assemblies from the user interface). I used fiddler to create a DELETE command. This was achieved simply by sending a delete request, similar to the one shown below:
From fiddler, go to the Composer window. Select "DELETE" instead of "GET" and enter the TeamCity URL in the form below:
http://<server>:<port>/httpAuth/app/rest/builds/<build ID>
You can find the build ID simply by checking the URL when choosing the build you want to remove from TeamCity (look for the number after the "buildId" query parameter). The only other step was to add an authorization header to the command. Type the following in the line below "User-Agent" in the request header window.
Authorization: Basic (Username:Password encoded as base64)
To encode your username / password as base64, go to Tools-> Text Wizard as a violinist and enter TeamCity data in this format - Username: Password. Finally, you must select the “Run” button, and everything will be fine, the assembly will be removed along with the Nuget package.
This worked for me, but obviously be careful when doing all this, since you don't want to remove the wrong assembly. It may be prudent to back up / snapshot the TeamCity server.
Hope this helps someone.