I don't know how the lower clergy of the MP feel about the OCA, but at the hierarchal level, relations could not be better. The OCA "Representation Church" (of St. Catherine the Great-Martyr) in Moscow has seen both official and unofficial, less formal, visits by His Holiness, Patriarch Alexy II, other MP hierarchs, as well as by ordinary MP clergy. And when MP hierarchs visit the USA now, the OCA rolls out the red carpet for them, so the warm feeling toward the MP is reciprocated by the OCA, at the official level at least, AFAIK.
That's good. Not surprising considering the symbiotic relationship between the two, and in fact those Orthodox churches that don't recognize the OCA as independent (autocephalous) see it as the US metropolia of the MP. In a way the OCA as such is the MP's creation. During Cold War d+¬tente, the American metropolia of Russian Orthodoxy (de facto independent since the 1920s and voted for in 1946, when it broke from nominal ROCOR supervision) reconciled with the Russian Church and the latter granted it independence, in 1970. Parts of the agreement, AFAIK, are: 1. There are to be no new MP congregations established in America. (I don't think anybody thought the Iron Curtain would disintegrate and Russian immigration would fill US MP churches.) 2. Congregations that, during the conflict, chose to be in the MP are to remain so. 3. Locally, in SCOBA, the MP is represented by its daughter, the OCA.