Cleaning Grease Off Z Axis

I recently started working in a media center where the Lulzbot machines had been unused for about a year. Both machines have issues going up the Z axis. I manually helped turn the rods and after a little bit they came loose and the motor was able to go up and down. However! The grease that’s on there is super tacky/ sticky and I’m sure it’s what was preventing the movement. What’s the safest/ least intrusive was to clean the old grease off before using the Lucas White Lithium Grease? I have no idea what was put on there prior, but it’s nasty and I think too thick. Thank you for any help.

When I clean my TAZ 5 lead screws, I take a tooth brush and hold it against the screw and run the axis up and down. The bristles will get into the threads on the screw and clear out the majority of the grease.

I will do this a few times followed by a paper towel or cloth to get more out. Understand that you will never get all of it out without completely removing the lead screws or spraying them down with something like brake cleaner (Do not do this).