Indeed, cutting someone's grass to show off may have a helpful product but is done so with selfish ambition and so is not good. The widow however should not suffer, her blessing is good, the mower's motivation however is corrupted. This of course is true for any day of the week. We also shouldn't mow someone grass on the Sabbath to make a statement and cause division all of which is has corrupted motivation.
Doing [good] in secret prevents most of this from happening because you can't show off when no one can see you do it.
But of course with the example of pulling sheep out of pits there is a sense of urgency with the act to save life regardless of who is watching. "Mowing" is a bit of hyperbole to push the point but the focus is still ministering to the needs of the lost as a mechanism to gain access so that we may pull them out of their proverbial pits.
If my neighbour is needing help, say single mom moved next door in a moving van with small kids set to unpack it all herself, then certainly I'm running over and getting friends to help to show her Christ in that moment of need and may I never say "sorry it's the Sabbath" to show her that Christ. We are all smart and can think of many real life examples of things like this happening.