How should one dispose of Jewish newspapers, newsletters, children's parsha sheets, etc. that contain Divrei Torah? I believe some poskim require/allow it to be double wrapped and then left outside to be picked up -- what is the reasoning behind that view? And is the halachah more stringent if parts of actual pesukim are quoted?
Excerpted from Rabbi Heinemann's guidelines (note that if something has an actual name of G-d, that's a separate set of issues; here we're assuming it's Torah but not the name of G-d):
How should one dispose of Jewish newspapers, newsletters, children's parsha sheets, etc. that contain Divrei Torah?
(I'd heard similarly from Rabbi Welcher. I think it helps that it's not an entire book/newspaper designed for teaching Torah, just a tiny piece of it. The respect due to Torah-teaching material is different than the prohibition of defacing the name of G-d; thus Torah material shouldn't sit with rotten eggs and coffee grounds, but if you double-bagged it that's okay. I think an RJJ article a while back proposed aggregating this type of sheimos and recycling it.)
(See the article for more.)
If I understand the article, I think it depends on the homework sheet. If it contains a large, direct quotation from Tanach, then yes. If the sheet itself teaches something, then yes. Otherwise not.
And is the halachah more stringent if parts of actual pesukim are quoted?
Yes if it's teaching Scripture; no if it's just Biblical paraphrasing to make a point (very common in rabbinic Hebrew).