How do I replace or refurbish the ink absorber?

You can remove it but HP is infamous for making them smaller than even Epson and Canon are now (even with chipped pads). Yours isn't terrible - yours uses the service station assembly so you do not have to touch waste ink (yay!!!) but yours also costs more to repair because HP has the service cap and motors in it and it adds cost (BOO!!!). The HP P/N is CM751-40001.

However, HP machines are a proper predicament to repair - unlike even the Epsons and Canons of the world with weak pad capacity, the procedures are KNOWN well enough we know the common ways, or we can get a leaked copy of the Canon/Epson service tools to repair the printers. HP doesn't have this and the procedure to reset is unknown. They skirt having to disclose this by replacing the printer and taking advantage of RtR laws that exempt the Amazons of the world from giving us the info by "replacing the product", so you also have a hard time finding the part. Unless it can be reset in the manufacturing mode or you can do home>? ~7 times (? 7 times brings up the support menu to do things like cartridge region swapping) you can't reset it due to the Amazon sized loophole HP has used for years. Yours nay never shut down but it’s a risk you run unless you reset the counter.

It may also be triggered by the following:

Home 3x (reads like a support menu, may not be useful)

Cancel>Resume>Cancel>Resume (support or diagnostic?)

iFixit has some guides for this but there's no info on how to bypass the ink system shutdown as HP has a real counter on these, whereas previous 564/920 machines were just allowed to flood with waste ink and you didn't have to mess with the WIC counter. It's not looking good in terms of finding a service manual.