My boyfriend still has the ambiguous messages from his ex-girlfriend. I asked him to delete them once, but I checked and still haven’t deleted them. What does this mean?

He wants to keep the memories with his ex-girlfriend.

Everyone has a past. If he deletes it at your request, he will have regrets in his heart and will think that you don’t care about his feelings, which will become a problem between you. It's better to let him bury his past memories deep in his heart, and use your sincerity to influence him, then in the end you will be his queen.