I see some Turbo Tax Document files with a "~" before the file name. What are these files?

Those are temp files. Leave them for the moment, because they come in handy for a recovery should your computer crash while you've got the TurboTax program open. Once you're done with your return and have filed it, you can delete all those files (and only those files) with the tilde character as the first character.

This is most common if you're using the desktop version of the program. But I'm a bit perplexed myself, as my screen indicates you are using the Online version of the program this year.

Thanks Carl. I'm using the desktop version. I've never seen this in the past with Turbo Tax. Started with some 2015 files and happening again with my 2016 files. They're not getting deleted automatically. I see this with some other programs but it's only when I have the file open. Once I close the file the program deletes the ~ file automatically. Not sure if this is a bug with Turbo Tax.

Could be with your OS for all we know. I've got that some years, not in others. I just delete them myself.