In this video I cover the process to change the ATF filter as well as the ATF itself on a 2005 Honda Pilot. Read full description for parts and details.

The process is similar but the filter is different (in the same location, but in a different housing) for 2003 and 2004 Honda Pilots. 2006 to 2008 Pilots use a different ATF filter (it looks like the part is 25450P4V013 but verify that from your VIN) setup all together.

Notes from the service manual about the procedure:
Check the fluid level 6090 seconds after shutting the vehicle down after reaching operating temperature.
Fluid drained at a level drain and fill should be right around 3.2 US qts.

Here are the parts used listed by item:

ATF Honda OEM ATF DW1 quart bottles (x4 (x10 for 3x flush (not filmed))
ATF Filter 25450RAY003
ATF Filter Housing Banjo Bolt Crush Washers (12mm) (x2) 9410912000
ATF Filter Housing Cap ORing 91301RAY004
ATF Filter Gasket 91302RAY003
Spring for ATF Passage 25803RAY000 (optional (I just got a fresh one to be sure))
ATF Drain Plug Crush Washer 90471PX4000

As for where to get those parts. I bought all the hardware from https://www.hondapartsnow.com and then got the DW1 ATF locally from my Honda dealer parts department.