My view differs from Gwens only slightly, and be aware that I am speaking as a native English speaker, not as a teacher.
I see "During our conversation..." as implying that at some point in time between the start and the end of our conversation (or now), an event happened.
Would you say there is not much difference between:
1-"During this converstaion, we took a wrong turn."
and
2-"During this conversation, we have taken a wrong turn." ?
I don't see much difference in the two forms. That, however, says nothing about whether they're both correct grammatically.
Red5
Webmaster, UsingEnglish.com