I’m assuming you mean McDonald’s the restaurant chain. I don’t see an obvious connection to the essay’s structure, but there’s a possible one in Teilhard’s defense of the Church as “the only international organization that works.” That makes his spiritual allegiance sound surprisingly like confidence in a successful global operation.

Dillard then brings that enormous institution down to the scale of one relationship: what do its rules mean for Lucile, who wants a life with him? Read through your comparison, the tension would be between an institution’s promise to serve everyone and its ability to meet a particular person’s needs.

That’s a tentative connection; your remark alone doesn’t establish which resemblance you have in mind.