Do I need to complete and submit the TM6 Departure Card when leaving Thailand for a DTV application?

Technically yes, if you received a TM6, it is still valid and you were still supposed to be putting the number on forms that asked for it. Some land borders are still handing out the TM6 cards.

I doubt anyone will say anything if you don't, but you are supposed to. At the bare minimum, remove it from your passport if you don't plan on handing it in to immigration, so it doesn't cause any issues in the future.

You don’t need. You can even remove it from your passport.

no.