What is the importance of a very tangentially related minor in grad school applications?
Except in unusual circumstances, a minor per se will matter for very little indeed in applying to graduate school.  There may be value in the particular things that you have done related to this minor (e.g., the field project) or reference letters you might be able to get due to your work towards it, irrespective of whether you actually complete the minor or not.

I would not however recommend delaying your graduation and grad school applications just to be able to formally complete your minor.