I'm on a server and I can't seem to be able to remove the table any way.

Only as the user changed the config value "protectTradingStations" to false o and it worked.

Alright, I'll close this issue then.

You can only break tables you've placed yourself. (You can change this from the config file. Note that it has to be changed from both the client and the server.)

If you're an operator, you can also /setblock it away.