Grumpy_Mike:
So you take the GND connector on one Arduino and connect it to the GND connector on the other Arduino. Do you not?
Oh, duh, sorry, I think I get it now. If I don't connect the grounds of each device together there isn't a complete circuit between them - it's just the TX pin of the Mega going into the RX pin of the Wemos.
But I would expect with a broken circuit to get nothing on the Wemos since there shouldn't be current flow, but it instead gets garble if there's no common ground.