"We write a letter to our grandmother."
Translation:Γράφουμε ένα γράμμα στην γιαγιά μας.
Those two are interchangeable. Of course, there is an emphatic issue, but you could say " Η γιαγιά μας/Η δική μας γιαγιά" in greek as well as you could say "Our grandmother/our own grandmother" in english (where Η δική μας γιαγιά and our own grandmother are the emphatic ones. Because in that case, you could may as well want to be emphatic and say that you're writing a letter to your own grandmother, and not someone else's. That's why there are two options. ^.^ ).