In ברכות פרק ד משנה ב we have נחוניא בן הקנה’s prayers upon entering and leaving the בית מדרש.  The משנה asks: מה מקום לתפילה זו, which from the answer given seems to mean what is the nature of these prayers.

From the only parallel use of מה מקום:

תלמוד ירושלמי מסכת יומא פרק ג דף מ טור ב /ה”ג

שאלו את בן זומא מה מקום לטבילה

it seems that the phrase means “what is the reason” for these prayers?  The answers can be construed as answers to either question.

In the context of the mishnayot about תפילות and the proper text and times for them, it strikes me that the question might be even more emphatic “What is the place for such a prayer?!” – that is, is it appropriate to be adding new (?) prayers upon entering and leaving the בית מדרש?  Is this the place for prayer? After all, we have a fixed (semi-fixed) liturgy and appointed times for prayer, and this is not one of them.  This is just a thought.