It is not possible to eliminate that completely without changing from 144 to a refresh rate that 60 divides into equally. If all other sources of stutter have been eliminated, this will always remain.
To get from your display refresh rate down to 60, OBS has to discard frames. To go from, say, 120 down to 60, it's easy-- OBS just discards every other frame. As long as all frames arrive on time, this will be as good as it can be-- not as smooth as the original, but a fair and reasonable, lower framerate facsimile.
Discarding every other frame of 144hz gives you 72 frames. So to get down to 60 in a second, 12 more frames have to be discarded. This cannot be done evenly, meaning that some frames will have bigger gaps between them than others, and although minor, this stutter will be both noticeable and, depending on the content, always present as long as the frame is moving.
So the ultimate questions end up being, have you removed all other sources of stutter (or, at least all those that can show up in the logfile, because this won't) and if you have, can you either live with this amount of stutter, or change your refresh rate to suit?