Assume the gentleman keeps his lip balm tube, at back of his Tallis bag probably with his handkerchief, and that he brings Tallis bag to Shul before Kabolas Shabbos & brings it home after Motzei Shabbos, so chances that he carried in street are exceedingly remote to say the least.
Then assume that what looks like lip balm, may have been tube of disinfectant & that maybe he had oral surgery this week, and must keep his mouth well disinfected. This is not remote thinking:- I had oral surgery this Friday 2 days ago, so these scenarios are more real than you goofus would care to believe.