This is the official explanation as written in the Watchtower Society's book "Insight on the Scriptures" Vol. 2, pages 55-6 (published in 1988). A bold-type heading reads, "What did Thomas mean when he said to Jesus, 'My Lord and my God'"?
"On the occasion of Jesus' appearance to Thomas and the other
apostles, which had removed Thomas' doubts of Jesus' resurrection, the
now convinced Thomas exclaimed to Jesus: "My Lord and my God!!
[literally, "The Lord of me and the God (ho Theos') of me!"]." (Joh
20:24-29) Some scholars have viewed this expression as an exclamation
of astonishment spoken to Jesus but actually directed to God, his
Father. However, others claim the original Greek requires that the
words be viewed as being directed to Jesus. Even if this is so, the
expression "My Lord and my God" would still have to harmonize with the
rest of the inspired Scriptures. Since the record shows that Jesus had
previously sent his disciples the message, "I am ascending to my
Father and your Father and to my God and your God," there is no
reason for believing that Thomas thought Jesus was the Almighty God.
(Joh 20:17) John himself, after recounting Thomas' encounter with the
resurrected Jesus, says of this and similar accounts: "But these have
been written down that you may believe that, because of believing, you
may have life by means of his name." - Joh 20:30, 31
So, Thomas may have addressed Jesus as "my God" in the sense of Jesus'
being "a god" though not the Almighty God, not "the only true God," to
whom Thomas had often heard Jesus pray. (Joh 17:1-3)"
I interrupt the quotation here to make a point. There is a suggestion that Thomas "may have" used that form of address because he thought Jesus was "a god" but not the Almighty God. They go on to give a second suggestion. I resume quoting:
"Or he may have addressed Jesus as "my God" in a way similar to
expressions made by his forefathers, recorded in the Hebrew
Scriptures, with which Thomas was familiar... [various scriptures
listed where a messenger of Jehovah was addressed as if he were
Jehovah God] Thomas may therefore have spoken to Jesus as "my God" in
this sense, acknowledging or confessing Jesus as the representative
and spokesman of the true God. Whatever the case, it is certain that
Thomas' words do not contradict the clear statement he himself had
heard Jesus make, namely, "The Father is greater than I am." - Joh
It is interesting that two suggestions are offered but no clear statement is made as to what the writer of the article goes by. Perhaps the readers (it is hoped) will combine both suggestions. The writer of the article is clearly going by the New World Translation, which only ascribes partial deity to Christ.