In my last parish, some people were involved with this movement. It’s a classic example of a fine effort which is hobbled by a well-meaning name which will permit people to pass over the experience without giving it a try. Plus, I should say that in the seven years my wife and I were in the parish, nobody ever invited us to a meeting.
Marriage Encounter, on the other hand, communicates decently well in two words what the weekends and follow-up are all about.
“Teams of Our Lady” communicates a Marian spirituality to Catholic couples who are “insiders.” To the unaware, it presents simply a Marian spirituality. Period. If I were on the board for ToOL, I would urge a name change. But with nearly seven decades of tradition, I’m sure there would be resistance.
Pope Francis mentioned something the other day about keeping the real Jesus hidden. It’s a challenge when our message, when the message of Jesus, is disguised.
Catholic Sensibility 
Never heard of Teams of Our Lady. Sort of sounds like Legion of Mary for couples. We did Marriage Encounter in 1980-ish. Found it a mixed bag. You had to wade through a ton of hokey-ness to get some good insights on communication and emotion. Hopefully it’s been updated since then.