Does there exists a simple HDMI pass-thru dongle that would allow a user to transmit text that overlays the video feed or blank the screen remotely?
Case use: We want to make sure my MIL takes her pills. All she does is watch TV. I’d like to place this piece of technology on her TV and then have it blank or show text on the screen to take her pills. Once she has taken them I would let the video feed resume. We are of course talking with her over the phone now.
AFAIK, not simple or cheap, no. Maybe put her DVR on a timer? 
No DVR, just Charter’s STB to TV.
I know Raspberry Pi has a HDMI out port, and a composite video (?). It should be simple to program that.
It’ll chirp & pop a message into the notification bar.
She’s a technophobe. (not counting the cable/TV)
Never really heard of such a device, no. Not sure how to approach the problem without throwing a lot more technology at it, which is usually the signal that a low-tech solution is preferable, sadly.
A watch, maybe? Or a take your damn pills timer?
They do related things to put a visual stripe on the field for football games, so it’s probably possible.
Simple, plug-n-play? Not that I’ve seen.
We’ve tried a kitchen timer. She doesn’t remember to reset it. The reminder clock would need to be reset with each day, something she’s not going to do.
Elder care can be so, so frustrating 
Sounds like you guys might just be SOL and have to stick with phone calls.
I’ll second the Raspberry or an Ardunio… You could hook into something on the TV stream (either the video feed, TV or if you’re lucky, pause the TV with a remote. I know they have IR interfaces available). Then it’s a simple process of building a script with a timer and wiring in a big alert button. TV is paused till you hit the button. If you wanted to go nuts, I’m sure you could get a pill caddy that you can monitor as well so you have to both take the pills and hit the button.
You could try one of those plug in timers, to turn off the TV when it’s time to take her pills and turn it back on 5-10 minutes later.
The annoyance factor might just be a motivator for her.
Oooh! You could even Autotune the audio channel for a couple minutes!
I know it’s @Nick_Burns’s mother in law 
, but no one deserves that.
I was once asked by a roommate to wake him at a certain time in the morning. I did so by yelling “fire” in his ear.
It might have been cruel, but it worked; I think he was fully awake and alert, not to mention out of bed, in less than a second. As an added benefit, we were able to determine that his heart could stand up to sudden, high-level stress.