Automatically remove e-mail from the recipients e-mail inbox when they have signed the doc?

We are using adobe sign for internal signatures, and one person is responsible for most signatures - they build up in his inbox and he cannot tell which ones are signed, and which are pending. Is there a way to have the e-mail automatically be deleted when the document has been signed? Or very distinctly marked? Right now he has to open the e-mail and click as if he were to sign - and then he is told it has already been signed.

I am of course looking for a function in the set-up in Adobe sign, when I send it out. Otherwise I will of course have to make the change in the e-mail client (which by the way is outlook, so if anyone happens to have an idea of how to fix it from that end, that would be wonderful as well).