Dogknox, I was a JW for about 25 years. The statements made by these JW’s at your door are not surprising and pretty much reflect what the rank and file JW would say to you. There is so much ignorance of history that one cannot expect them to respond with anything other than what they fired back at you.
I know you probably don’t have access to this, but JW’s have a two volume Dictionary/Encyclopedia that they themsleves publish called “Insight on the Scriptures” (it used to be called “Aid to Bible Understanding”,you can find free PFD downloads online) that they use for reference material for subjects such as what you were discussing with them. Of course, the “history” presented in these publications are very biased and rudimentary. Under the section called “Canon” in volume 1, the book states that the canon of scripture was closed at the end of the 2nd century, but cites no source as evidence for this and expects the reader to take their word for it. They also name individuals such as Ignatius, Irenaeus, Polycarp, Justin Martyr and many others in this section (in a positive manner too), but don’t reveal who these men really were. It could be quite enlightening for them (it was for me, but I was searching) to see some of Ignatius quotes, for example, and show them how he names the Catholic Church in about 107 AD. Starting with history could plant a seed.
Something you could show as well:
“Catholic is the Anglicized (English) version of the Latin word Catholicus which is a Latinized version of the Greek word: καθολικη, transliterated into our alphabet as Katholikos. Katholikos means universal and is derived from kata (throughout) and holos (the whole).
In Acts 9:31, the Greek phrase: ekklesia kath olos, translated as “the church throughout all” (RSV) or “the church everywhere” (NCV), seems to me a likely origin of the phrase “the Catholic Church” (katholikos ekklesia) first documented in Ignatius of Antioch’s letter to the Smyraeans in A.D. 107.”
Acts 9:31 (RSV)
So the church throughout all Judea and Galilee and Sama’ria had peace and was built up; and walking in the fear of the Lord and in the comfort of the Holy Spirit it was multiplied.
So, you could show them that “Jehovah’s Witnesses” aren’t mentioned in the NT, but here we have this description and ask what they make of that.