It’s just different translations. I am no Latin expert, so if one were to come here it would be of great help. The phrase in question is “dum praedicatur et colitur.” Praedicatur is that part being translated as ‘preaching’ or ‘proclaimed,’ and colitur is the word which the real question is over.
From what I can tell, the word can mean anything from cherish to honor to worship. Here is where it gets a bit tricky, because Latin words often mean several things for which we would use different english words, and so determining the proper translation is not always a science so much as an art.
However, in this case the situation is a bit different because we are dealing with a Church document. The Church does not use Latin as it is learned in high school or college, but a slight variant known as ecclesiastical latin. This is not so much a different language in and of itself that was chosen, but rather the result of centuries of development. Over the past two millenium, the Church has selected to use certain words to refer to certain things. In other words, at one point the Church decided that whenever they wanted to refer to Heaven, they would use Latin word X, whereas that word may normally refer merely to the sky. In order to know for certain what it means, someone would have to have an ecclesiastical Latin dictionary, which I unfortunately do not.
The point to all of this is that ‘colitur’ most likely means ‘honor’ or ‘venerate,’ and some people simply failed to translate it appropriately. Or, the Church may have no special use for the word, and it may simply mean anything from cherish to honor to worship, and whoever translated your version preferred to render it as ‘worship’ in the traditional sense (which was, as was explained below, not reserved for divinity); many people prefer this traditional usage to words like venerate, particularly traditional Latin Mass only style Catholics (as well as others, of course).
Fortunately, the question is not that difficult, and does not require documenting the usage of Latin over the ages to respond to. All that is required is to provide a basic explanation of the traditional usage of the english word ‘worship,’ explain the possible meanings in Latin, and then point them to read the rest of
Lumen Gentium, which makes it clear that Mary is not divine and is subordinate to Christ. They will then have to either abandon their attack or make the ridiculous assertion that the authors of a document teaching not to worship Mary then indicate within the same document that we are to do just that.
