How do I turn off the hardware monitor on UR44?

Have a look at your signal chain. I am assuming your pitch shifter is in reaper. I will assume you’ve got your guitar plugged into say HI-Z input 1 of the UR. If you check the signal flow, this signal is split to Mix 1 and 2 as well as to the DAW over USB. The phones 1 is hardwired to mix bus 1 (Phones 2 can be selected between the 2 mix busses). If you just want to hear the shifted (i.e. processed in reaper) output which is controlled by the DAW fader (2nd from right on the dspMixFx mixer, then you also need to turn the fader for Input 1 all the way down (or better yet mute it). This will ensure that only the processed signal will be heard and none of the live dry guitar.
Hope this helps.