The first few model years of the first generation Mazda 6 (2003 to 2005) came with a feature that allowed the vehicle owner to disable the remote boot release button on the keyless entry fob. On later models, this feature was removed. You can disable the boot release function on the keyless entry system; however, you'll still be able to open the boot using the inside boot release, which is located beneath the steering column.
Sit in the Mazda 6. Open the glove box in front of the passenger seat.
Inspect the left side of the glove box compartment. You'll see a button labelled "Trunk Opener." This is the button you'll use to disable or enable the boot release.
Push the button to disable the boot release. When the button is in the "Out" position, the boot release is disabled. Push it again to enable it. When the button is in the "In" position, the boot release is enabled.