According to McLuhan in a late (May 6, 1969) letter to Jacques Maritain: 

My first encounter with your work was at Cambridge University in 1934. Your Art and Scholasticism was on the reading list of the English School. It was a revelation to me. I became a Catholic in 1937. (Letters 371)

As discussed here, in 1934 McLuhan may already have been in touch with Maritain’s colleague and friend, Father Gerald Phelan, and may well have started to read Maritain on Phelan’s recommendation. Since McLuhan arrived in Cambridge in the fall of 1934, his reading Maritain in his first term there at the time of his initial exposure to Eliot, Joyce and Pound, may hint in that direction. Absent such stimulus, it is hard to imagine that he would have had the motivation and time to do so. Similarly with his citation of Maritain in his Chesterton paper (written in 1935) since Phelan almost certainly arranged the publication of that paper in The Dalhousie Review. Similarly again in his note to Maritain that “I became a Catholic in 1937”, an event guided by Phelan. 

As shown by a letter to his family in February 1935, McLuhan also read another book of Maritain in the first months he was in Cambridge, one that would not have been “on the reading list of the English School”:

As a handbook on Philosophy with especial regard to its historical development, I strongly commend Maritain’s Introduction to Philosophy to you, Red. He is the greatest living French thinker and is one of the foremost students and interpreters of Aquinas. Like most French texts it is a marvel of lucidity and order. I have read or dipped into numerous histories (all of which supposed Augustine and Aquinas were spoofers) and which therefore misunderstood everything that happened in society and philosophy after them. It is for his sympathy in this matter as well as his general account that I recommend him to you as certain to prove most coherent and stimulating. (Letters 53) 

A quarter century later McLuhan reviewed a new translation of Art and Scholasticism in his only other appearance in The Dalhousie Review. Here he identified what must have been so important to him in Cambridge:

Maritain’s familiarity with the work of the symbolist poets and the painting of his time provided him with a sensibility that gave him access to scholasticism, not as an historical, but as a contemporary, mode of awareness. (Dalhousie Review, 42:4, 1963, 532,)