Short answer from the writer Kim Eun-sook (YouTube):
it's when he was having the triangle gimbap that he realized that he liked her.
Longer answer:
In an earlier episode, Dong Eun asks Do Young to leave his wife Yeon Jin.
I hate to say I don't know but I don't know yet.
I just realized I’ll never leave her. So, let’s meet again.
(Note that Do Young has been portrayed as someone who is very decisive and makes decisions quickly and firmly.)
Writer's comment (same YouTube video):
He says that he doesn't know although he hates saying that. I think that line conveys his feelings pretty well. ...
He's only useful to Dong-eun if he's still Yeon-jin's husband. If he leaves Yeon-jin, he has no reason to meet Dong-eun.
He wasn't sure how he felt about her back then. I think it's when he was having the triangle gimbap that he realized that he liked her.
I'd add a bit more:
Do Young was previously someone who would never eat at a convenience store, while Dong Eun is someone who regularly does so.
So, this scene also expresses that he's become fully converted to Dong Eun's point of view. Just having visited his wife in lockup, he now fully understands how evil his wife was and is and how Dong Eun's actions were fully justified.
He should and does play his role as "The Glory". He helps Dong Eun kill Jae Jun, then abandons his wife, leaving Korea for England with his daughter. (Note: It is also confirmed by the writer in the same YouTube video that he and Dong Eun planned Jae Jun's death together.)