I'd probably go with something on the lines of:
Hi [whoever]
Just checking that the XXX I sent you on Xth XXX is okay. I have to [do something] with your feedback before I can [do something else]. Can you let me know when you'll be able to look at it for me?
Thanks
That way, it makes it sound like you're putting yourself in their debt (whether or not that is true is irrelevant), and people on the whole tend to like people being indebted to them.
It also doesn't actively demand that they do something immediately, just asks them when they will be able to do it.