Tsubame Gondolier

One day, a small boat drifted to a certain remote island. The man who was on board was a yakuza full of wounds. May Tsubame lives with her grandmother who runs a general store on the island. A former office lady who has just returned to the island without finding a place in Tokyo. Tsubame takes care of the wounded drifter without leaving him alone.
There's no place for an ex-office worker and a wounded gangster. The days of searching for a place start on a remote island.

(Source: Shodensha, translated)

Note: Includes 1 extra chapter.