Stop using anti-Catholic websites as your sources and actually go to a university library. There are 15 extant letters allegedly authored by St. Ignatius. the seven epistles of Ignatius of Antioch were forged in the 3rd or 4th centuries. The other 8 are genuine. (note: The fact that some would seek to have forgeries associated with St. Ignatius only reinforced the value of his legitimate letters.) The term Catholic was used in The Epistle to the Smyrneans, one of the eight legitimate letters.
The term was also used by other second century authors in the Martyrdom of Polycarp, written in c. 155 AD, and in the Muratorian fragment written in c. 177 AD.
Peace be with you
Ignatius did not use the term Catholic...He used the term catholic...You want to tell what set of letters contain the term Eucharist???
And also:
The word Catholic (katholikos from katholou — throughout the whole, i.e., universal) occurs in the Greek classics, e.g., in Aristotle and Polybius, and was freely used by the earlier Christian writers in what we may call its primitive and non-ecclesiastical sense. Thus we meet such phrases as the "the catholic resurrection" (Justin Martyr), "the catholic goodness of God" (Tertullian), "the four catholic winds" (Irenaeus), where we should now speak of "the general resurrection", "the absolute or universal goodness of God", "the four principal winds", etc. The word seems in this usage to be opposed to merikos (partial) or idios (particular), and one familiar example of this conception still survives in the ancient phrase "Catholic Epistles" as applied to those of St. Peter, St. Jude, etc., which were so called as being addressed not to particular local communities, but to the Church at large. http://www.newadvent.org/cathen/03449a.htm