You can't expect a precise measurement for an imprecise concept, but here's an approach that might sort of work.
Holding the gripper, mark a point between your middle fingers for one side, and somewhere that your palm touches the other side of the gripper for the other side. Since you grip at an angle, you get different leverage at different parts of the handle and you need to pick one part of the handle to make your measurement.
While holding the gripper closed, put some rubber bands at the marked spot. You can't get them all precisely there, but just do the best you can.
Release the gripper and measure how far your rubber bands let it open. Do this repeatedly.
Remove the rubber bands and make something else to stretch them that you can measure, like suspend a bucket from them and measure how much water it takes to stretch them the same distance. Try to get the handles the rubber bands are attached to be the same diameter as the ones on the gripper. Do this measurement repeatedly.
Check whether the rubber bands get significantly weaker with repeated stretching, by looking for doing a least-squares on the two sequences of measurements, and see whether the slope is significantly different from zero. If it is, and if you want some sort of precise value, then you should repeat the trials enough to get your slope estimate as precise as you want it, and then correct for that.
If your rubber bands are too weak, then get stronger rubber bands. Varying thicknesses of some sort of inner tube, maybe.
It sounds like your gripper has a way to adjust the resistance over a wide range. Unless it clicks across quantum adjustments, likely adjusting the thing will provide big errors. It might be hard to adjust it the same way twice, to the point that you needn't care about precision better than that.