Is there a Halachic or Hashkafic problem with a single post-sem girl working with mixed teen groups?
Your question assumes that this is only a problem for a single girl. There can be serious issues with such a setup to begin with, even for married people as well.
Because there are so many facets to this question and there are multiple situations which can arise, a Rov who is familiar with the particular situation and circumstances needs to advise you as to what is acceptable in the particular situation you’re asking about.
As a general rule, teens may not be mixed in any setting, even for Kiruv purposes. There might be room for an exception in unique situations, which are extremely rare, where this is the only way to save them from intermarriage, assimilation or in a situation of Pikuach Nefesh.
ראה הנלקט בשליחות כהלכתה מהדורת תשע״ו מדור תערובת אנשים ונשים בעת שיעורי תורה, ע׳ 122 ואילך. ושם מדור פעולות ראויות וכו׳ ע׳ 124. מדור עניני חינוך עניני הלכה ומנהג ע׳ 748 ואילך.