Ha Rav, I covered urine on the floor of the Shul toilet with a paper towel . I then inadvertently stepped on the paper towel, was it Chillul Shabbos for S’chitah (squeezing)?
In retrospect we will not say that it was chillul Shabbos. Sechita can be one of two melachos, either melabain, because squeezing the liquid out of clothing is making the clothing better, or dosh, which is squeezing the liquid out because it is needed. In this case you do not want to make the tissue any better, and it isn’t being made better. You also don’t want to have the liquid that was squeezed out, therefore it isn’t any of the two melachos, and permitted. Additionally there is the mileches machsheves aspect. You did not intend to squeeze the paper towel, in fact you didn’t want the liquid to leave it. Therefore, it was a psik riesha d’lo niecha leh. Together with the backhanded way of squeezing the paper towel, (shinui). Additionally, the paper towel is not getting cleaned by your stepping on it, and you have no intention that it get cleaned, and it isn’t the norm to clean a paper towel.
שו”ת אגרות משה אורח חיים חלק ב סימן ע’ “מ”מ כיון דאינו בתוך כלי וגם אין דרך לסחוט מים מנייר כלל לא לצורך המים ולא למלבן ואינו מתכוין לזה יש להתיר”.