I can't take credit for this.  I found it on Spectrum and it worked for me, so passing it along:
https://robertsspaceindustries.com/spectrum/community/SC/forum/3/thread/3-4-3-pu-update-not-registering-in-launcher-resolu
								- Perform Launcher Reset : [ Ctrl+Alt+Shift+R ]
 - Confirm
 - Kill launcher in Task Manager
 - Reopen Launcher
 - Install 3.4.3
 
https://robertsspaceindustries.com/spectrum/community/SC/forum/3/thread/3-4-3-pu-update-not-registering-in-launcher-resolu