should you remove the seed pod when deadheading petunias etc

The flower becomes the seed pod, so if you remove the flowers, then you're removing the seed pod as well. Unless you're talking about ones you've missed that have turned into pods. The point of deadheading is usually to prevent the plant from producing seed - many plants, once they've done that, stop flowering, so removing that encourages more flowers. What did your friend think you should be doing, and why, I wonder.

Yes you should, the whole point of dead heading is to remove the seed pods (heads being seed heads).

Removing the old petals will tidy the plant up but stopping the plant producing seed (removing pods) will make the plant produce more flowers and therefore try and make more seed (as stated above, really need to read posts properly!)

unless you want seed for next year. i wonder if this is what your friend has in mind.