PCN timed at 16.19, so well outside any possible de minimis consideration, but it would still be a good idea to submit representations to Tfl. There are serious flaws with TfL management of enforcement so I expect you will soon hear from the experts on this aspect. In addition, there was your unwell passenger who apparently needed something quickly from a pharmacy.
Unfortunately your narrative about people in the car, engine running, only 6-7 minutes is irrelevant, but being from outside London might get you a few plus points with TfL. Do be aware that TfL, like the London councils, make millions from parking enforcement, so are not usually minded to give way on arguments based on mitigation, as they want your money !
So don't pay yet, and wait for further advice, but don't miss the pay or appeal deadline date.