Remove the regulator handle clip using a rag as shown.

Inner handle removal/installation
Regulator handle installationMazda 6 Service Manual: Manually Shifting Up
You can shift gears up by operating the selector lever or the steering shift
switches (some models).
M1 → M2 → M3 → M4 → M5 → M6
Using selector lever
To shift up to a higher gear, tap the selector lever back (+) once.
Using steering shift switch (some models)
To ...
Mazda 6 Service Manual: Auto Lock/Unlock Function
WARNING
Do not pull the inner handle on a front door: Pulling the inner handle
on a front door while the vehicle is moving is dangerous. Passengers can fall out
of the vehicle if the door opens accidentally , which could result in death or serious
injury.
When the vehicle speed exceeds 20 ...