"We praise our parents."
Translation:Noi îi lăudăm pe părinții noștri.
I'm confused. Sometimes, following 'pe', the definite article seems to be required and sometimes it doesn't. Does this have something to do with the presence or not of a modifier - in this case 'nostri'?
That's correct, the pronominal adjective "noștri" makes it necessary to have an article. You can drop the enclitic article and use the possessive one instead: "noi îi lăudăm pe ai noștri părinți", though it sounds less natural.