From the 98107 manual:
"The sensor should be kept moist at all times. For this purpose, always keep wet the tissue inside the protective cap. In case of erroneous readings even after an accurate conditioning and calibration, the reference junction might be contaminated or clogged."
That is followed by the reference strip trimming procedure.
I interpret the above as meaning you only do the strip pull-out & trim thing when you are unable to manually calibrate the meter after obtaining erroneous readings (how you determine <= that is a whole 'nuther question).
As for the sponge, tissue, whatever, the cap for my Hanna 98128 came with neither. An email to their support department returned the advise that a few drops of storage solution in the electrode well within the cap was sufficient and no sponge was required...