In another article on this topic of Midrashic typology in the NT,
https://www.biblicalstudies.org.uk/pdf/eq/1979-1_022.pdf
An early effort is made to explain the use of the word in a footnote:
1 It is not the purpose of this article to propose a precise definition of the terms midrash and midrashic. For a discussion of this problem see Le Deaut, "Apropos a Definition of Midrash," Int. 25 (1971) pp. 259-82, and Wright, "The Literary Genre Midrash," CBQ 28 (1966) pp. 105-38,417-57. In this article the term midrash will be used rather loosely. We will be considering many NT passages which comment upon the OT; such passages are "midrashic" in at least the etymological sense of the word, regardless how much they may differ from the halakhic or haggadic midrash. We need some term by which to refer to such passages, and "midrash" seems a logical choice. Some writers use this term in a different sense. For example S. Sandmel (The First Christian Century in Judaism and Christianity [New York: Oxford, 1967] p. 188) speaks of the gospels as a midrash on the life of Jesus. But in this article the term will be restricted to passages which comment upon the OT.