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