I couldn't find the Remote Tool Update 3 on MSDN (@wblanks - it would have been nice to post a link, although I suspect that even if you did, that link may not be available anymore, as I searched MSDN for this update and could find it).
However, I had Visual Studio 2015 Update 3 installed on my development machine.
In the C:\Program Files (x86)\Microsoft Visual Studio 14.0\Common7\IDE\Remote Debugger
folder I found the msvsmon.exe
version 14.0.25420. I copied the entire content of the Remote Debugger
folder over the Remote Debugger
folder on my tablet, where I had initially installed the Remote Tools for VS 2015, Update 1. After that, I restarted the Remote Debugger app on the tablet and when I tried to deploy my app remotely from Visual Studio 2015 running on my development machine, I no longer got the DEP4300 error.