Question [Q] Failed 4.4.3 OTA update

I have a rooted Nexus 7 (2012) with stock Android 4.4.2 (Build KOT49H). I have TWRP installed. Recently, I got a OTA update notification, which I chose to install. After downloading it, the tablet requested to reboot as usual, but it rebooted into TWRP and just stayed there. I had to select reboot in the TWRP menu. The tablet is still in 4.4.2 and now it doesn't notify me of any OTA (it just says "Your system is up to date").

Should I flash stock recovery to install the OTA?
Is the downloaded OTA still somewhere in the tablet?
How do I get the tablet to recognize the OTA again?