The answer: When in doubt, throw it out.
What if I recycle it? The ACC Solid Waste Department needs clean recyclable materials. If too much grease or fat residues are on the container, it can contaminate the collected materials and reduce the market value. When in doubt, throw it out.
What if I wash it out first? Washing out containers made from recyclable material uses water, so not necessarily the best when trying to reduce water use. However, the water use can be offset by the water saved through the reuse of recycled materials vs. the water cost of using virgin materials. If you are efficient with your rinsing and it is a fairly clean container, the water savings of recycling should outweigh your water used for rinsing. Go ahead and rinse. If it is very dirty (think hot fudge glass jar), throw it out.