Can I reverse my Logitech keyboard's touchpad scroll direction?

Short answer: No, not in SetPoint.

In a relevant post in the Logitech forums from 2013 August 8, a Logitech support technician states

This is not an option in Logitech Setpoint for Windows either.

This was my experience, today. Based on another forum post from a different Logitech support tech, I installed SetPoint in an attempt to accomplish the same goal (reverse scroll direction on a Logitech K400 wireless keyboard/touchpad combo) and fiddled with it for a couple of hours.

Long answer: Yes, if you are willing to do some registry surfing.

The technician goes on to cite a registry edit "for the sake of information". Specifically:

Registry Path: HKEY_LOCAL_MACHINE > SYSTEM > CurrentControlSet > Enum > HID > VID_046D&PID_C52B > Device Parameters (All)

For Vertical Scrolling: All Device Parameters
Entry Name: FlipFlopWheel
Control Value: 0
Reversed Value: 1

For Horizontal Scrolling: All Device Parameters
Entry Name: FlipFlopHScroll
Control Value: 0
Reversed Value: 1

Then, the tech discourages the reader from manipulating the registry. Reasonable advice, considering that the suggested edit is not straight-forward.

I am using the Logitech Unifying Software on Windows 10 and have additional pointing devices attached through the unifier and otherwise. At HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Enum\HID, I found 18 member keys with names that started with VID_046D&PID_C52B but continued with additional specifiers. I.e. by studying the values in the subkeys, I eventually determined that my Logitech wireless trackball (a separate device) was represented as:

VID_046D&PID_C52B&REV_1203&MI_02&Qid_1028&WI_02&Class_00000004

and the trackpad component of my K400 was represented as:

VID_046D&PID_C52B&REV_1203&MI_02&Qid_4024&WI_01&Class_0000001E&Col02

Each of these keys has a complex-looking subkey that itself has two subkeys: Properties (protected against access) and Device Parameters, the one we are looking for. On my system, the particular FlipFlopHScroll and FlipFlopWheel that I wanted were found in:

HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Enum\HID\VID_046D&PID_C52B&REV_1203&MI_02&Qid_4024&WI_01&Class_0000001E&Col02\8&262edd47&0&0001\Device Parameters

If you can identify the correct path for your setup, right click on the two FlipFlop data elements (to Modify... in regedit) and change them from 0 to 1. I noticed the desired effect after I restarted my machine.

To aide your search, try searching the HID key for the string logitech. The 'complex-sounding' subkey for the appropriate subkey of HID will have some helpful info. Specifically, my

HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Enum\HID\VID_046D&PID_C52B&REV_1203&MI_02&Qid_4024&WI_01&Class_0000001E&Col02\8&262edd47&0&0001

has the data element named DeviceDesc with the value

@oem23.inf,%hidcordlessunifyingmouse%;Logitech HID-compliant Unifying Mouse

On my system, this was one of two such keys. (I have two mouse pointers managed by the Logitech Unifying Software.)

Wow....Logitech Options software is a 201MB download. Which is a behemoth just to change a registry key. :\

Well I went ahead and tried it, on Win7, for my K400. The software seemed to be only looking for a K400+, so it never could find my K400. It also introduced a phantom "stuck arrow key". So I had to pull the dongle out and de-install "Logitech Options". Then that problem went away.

So I had success with the direct registry edit, described above. However, I recommend an easier way to find the correct key:

1. Physically pull out all Logitech input devices, except the keyboard.
2. In Device Manager, double-click MICE > Logitech HID-Compliant Unifying/Cordless mouse.
3. Click on the DETAILS tab
4. For PROPERTY drop-down, select HARDWARE IDs
5. Right-click and copy the first value in the list. It should look something like... HID\VID_046D&PID_C52B&REV_1210&MI_02&Qid_4024&WI_01&Class_0000001E&Col02
6. Open up REGEDIT.EXE, and right-click on HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Enum and choose FIND...
7. Paste into the FIND criteria box, and click OK. Open up the DEVICE PARAMETERS sub-key and that's where you add/edit the DWORD values, as per above post.
8. Pull out and in again, your logitech dongle, then turn off and on the keyboard, and voila!
9. Reinsert any other dongles you removed in step 1

{Mod: I couldn't find a way to ask for my edited answer to be re-instated, nor was told it would automatically be reconsidered after the edit, so I've gone ahead and re-posted this as a new answer. Please let me know if I'm missing something, as I'm new hear and keen to learn how things work. :) }