The Workspace Studio should only ask if you want to save a tab if it has changed. Starting a new gadget on a new tab technically means opening a new tab and then changing it by adding a gadget to it. Therefore if you close the tab without making changes to the gadget the tab itself was still changed so will ask you if you want to save. We have looked into detecting that case but that requires us to guess the user's intent when creating that tab. They may be making a template they want to save for later.
There is currently no way to stop the line being added to the telnet/ssh copy. We can log that as a feature request and look at putting it on our product road map.