No, there is no sin involved at all. In fact, what the Greek Orthodox believe is very similar to what all Catholics believe. It's our prayer that over the next few years we can come into full communion with each other.
If this were a Protestant prayer that explicitly had prayer lines that contradicted Catholic teachings, that would be another issue.
For a sin to be a mortal sin, it must include all three conditions:
- It must be a grave matter. (e.g. based on the Ten Commandments)
- We need sufficient time to reflect upon the sin we are about to commit
and then must make the decision to sin anyway.
- We must give full consent of the will to commit the sin.
None of this happened in your case.
- Do I have to mention what happened the next time I go to Confession?
No you don't, but if it is something that bothers you, you can bring it up at the end of your Confession in conversation.