There is only 1 screw. The back side is just a metal tab which slides into the metal bracket, as I recall. Per the schematic, all that is inside that "blower auto-speed" box is an array of relays. I don't think the box itself decides upon blower speed, but has an array of command lines (~6) which come from another box, like the silver "TemperatureRegular" box next to it, though could be and/or the pushbutton box. The schematic should tell you.

While "in there", you might consider doing as I did and power that box via a new 12 awg wire direct from BAT+, with an inline fuse. You can easily push the wire thru the grommet below the battery tray (can work blind). The reason was that the high blower current may otherwise melt the #8 fuseholder if there is any resistance from corrosion. You see that in many of these cars in the junkyard. My 1985 300D had that problem, which appeared due to it having a special crimped part below the #8 fuseholder. I measured high resistance across that piece (google my post w/ photos). Not true on my 1984, though I rewired it similar just in case. That is also a much shorter path from the battery. I don't recall wiring a relay in there, since that power wire is always hot (recall). If switched, I would have.

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1984 & 1985 CA 300D's
1964 & 65 Mopar's - Valiant, Dart, Newport
1996 & 2002 Chrysler minivans