How do I see which tax returns have been efiled?

Probably the easiest method is to open the Efile menu, select Reports, then select Current.
You are now shown your efile log.  Note the window on the bottom of the dialogue box shows a summary of the file selected.  If you select the top file, you'll see the name appear in the display box at the bottom of the box.  Use your down arrow key to move down the files while watching the name change in the bottom view box until you find the file you are looking for.  You an also double click the file to open it and see a larger screen of the same message.

A fast way to look up the exact date and time the file was transmitted is to open the file, click the Save button, and review the save log that appears in the dialogue box.  This log shows the date and time the file was e-filed and whether the file was Accepted.  You can then use the E-file Report log to find the file matching that time specific time.

Hope this helps. 

Why not just show the "open File" which lists all the clients that have been opened. select you client's name and in the lower box of that file it shows you all the info you need- opened, efiled, accepted etc. (and shows the time and date

I was going to suggest that option too, Bill, and quickly checked out my version before submitting my reply.  However that "Preset" preview wasn't enabled on mine and I didn't think to look in the PRESET pull-down to find it.  I instead glanced in the "Custom Formula"s menu and didn't initially see e-filed status there.  Thanks for poking me to go back and look again.

The other way to see the efiled Returns is to go to "open" which shows all the files and unselect all the selections in the right hand boxes (under efile status) except for "accepted". That shows all the accepted efiled Returns.

I don't see that option, Bill, in my 2019.4.0 release of Profile T1.
In the Open File menu, in the upper box, only the Client Name, File Size, Item Type, and Date Modified parameters are listed.  I see no options anywhere to add more fields or to change those fields.  Clicking on the top status bar does nothing.  Right clicking in the upper client display box only gives the options to view Large Icon, List, or Detailed.  It would be nice to customize that large window to be used like a database and shows only the e-filed files, but that option doesn't seem to exist on my version.
Same thing with the lower display box, the only option is Preview and Open in Read-only mode.   And right clicking in that box shows "add preview item" and in that menu, there are no options to unselect all selections in right hand boxes except for "accepted".   Are you sure you aren't talking about the Database itself because those options exist in the database and that's my normal method for checking this stuff.