I assume they are talking about the splash guard / aeroplate underneath the engine which helps with MPGs to some extent. The plastic engine cover doesn't even need to be touched during an oil change.
Look up the plastic clip part numbers on a Honda parts site, then cross-reference them via eBay or Amazon to get a significantly cheaper knock-off. I've been able to get a bag of 20 for the price of 1 bought from the dealer parts counter. If they don't last, well you have plenty of spares now.
They reduce wind noise, increase mileage particularly in colder weather (and speed up engine warmup time), protect the engine from road debris/road salt/water, and reduce lift generated at highway speeds.
"Trapping heat in" isn't a problem in almost any modern vehicle.
But yea, completely non-functional. Remove it if the clips are broken. You aren't missing anything.