My thought is the caliper mounting surface is slightly canted (couple of thousandths) on the forward edge. This would cause the pads to wear slightly more on the front edge vs the rear edge.
When you stop with your foot on the brake and put it in park, the pads are squeezed against the rotor and come to rest. This is a substantial amount of hydraulic pressure, normally when you remove your foot off the brake, the residual hydraulic press bleeds off and the “barrel” side pad retracts slightly, removing the “pinch”.
Since there is an electrical parking/hold function I believe that system’s not allowing residual pressure to 100% bleed off (even tho’ you didn’t press the button). Those couple of thousandths difference between the front and back edges of the pads are creating a knife edge against the rotor at the rear of the pads and when you back up, that knife edge is scraping the rotor creating the horrific sound until you put it in drive and release the brake (I keep my foot on the brake when in reverse). The rotation of the rotor with no brake applied will naturally realign the pads to the same plane as the rotor and the sound goes away.
By backing into my parking spot and when departing the next morning, my foot is on the brake, shift into drive, release the brake and the rotor immediately starts rotating, thus realigning the pads (knife edge no longer making contact) and in my case …… no horrific sound.
A stainless spring steel shim may help alleviate the non-100% bleed off of the hydraulic pressure due to……. when it cools, it’ll shrink slightly and allow more space between the pad and the rotor.
Just my theory tho’
(edit) LEXUS TSB adds a 2nd spring and new rotors (probably harder material) and pads.
View attachment 41706
The following is a break down from the LEXUS TSB. They specify rotors with a "Gold" dot.
Disc Front, 43512-0C040 - $86.39
Disc Front, 43512-0C040 - $86.39
Pad Kit Disc Brake, 04465-34040 - $109.32
Shim Kit Anti Squeal, 04945-0C060 - $32.96
Disc Brake Anti-Rattle Clip Set, 04947-60140 - $7.25
Brake Caliper Grease, 08887-80609 - $25.38
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