The shot of Nat & Kat is from Ep10 when they are getting on the ferry to Cheung Chau island.
What they are wearing is a perfect match* to the Cyprus confessional (Cyprus is the type of tree in the shot) when they talked about the restaurant fake food.
*almost: the exception is that Kat no longer has the blue sleeveless under her black shirt.
You can see the top right strap of the blue sleeveless in the ferry shot. It's under the backpack strap. But things change! After they get on the ferry, and for the rest of the leg, the Kat is without the black shirt. Even the confessionals shot in the hotel room show this clothing configuration.
Since the Cyprus confessional is in good daylight we can conclude that it was shot on any date after the Hong Kong leg:
June 13th in Hong Kong possible
(long pit stop since they aren't spotted in Seoul until the 14th)
June 14th in Korea (not likely due to type of tree)
June 15th in LA area possible