Recommendations for rinsing recyclables?

Can't find any info online so just wondering what other people are doing.

I have been trying to do meals with items that are low water intense right now but was obliged to make a large pasta thing for work a few days ago... read: lots of tomato and pasta cans on the counter.

Are we just tossing them in the blue bin unrinsed or is it better for the recycling facilities if we're just tossing anything harder to rinse (like peanut butter and mayo jars too) into the black bin for a few weeks?