They might be referring to the university subject. I think the context is not enough. "ÎγÏαψα" can also have the meaning of "I took the exam/test..." What do you think?
"ΈγÏαψα" could mean that but not if followed by "με". I don't know. It doesn't make much sense no matter what way I look at it. "I took the test for Metafrasi" would be:
ΈγÏαψα ΜετάφÏαση.
or maybe even
ΈγÏαψα τη ΜετάφÏαση.
That "με" really breaks the meaning...
It's like it says that they wrote (something) using the "Translation". Or they wrote (something) along with the "Translation".
I completely agree with you. It doesn't make sense due to lack of context. Therefore I'd go for your last version, "I wrote (something) along with the "Translation", where you've cleverly overcome this tricky "με" situation by using "along with". What do you say?
There is also the chance that this was "εγÏάψαμε την μετάφÏαση" and some auto-correction put a space in there and corrected the accentuation. That's actually the most probable explanation now that I think about it.
I just tried this with SwiftKey on Android. I typed in "εγÏαψαμε" without any accent and without space, and the suggested correction (which would be selected if I pressed space) was "ÎγÏαψα με".