I would definitely recommend asking.
About a week or two after their visit, I send a follow-up e-mail to let them know the damage deposit has been refunded.
I include a link to either the listing site they came with or my homeawayconnect site if they would like to submit a review. (I agree that making it easy for them is the best idea.)
Every now and then, I leave out the review request and send a feedback form (based on one kindly provided by an LMHer!) so that I can gauge what works and what doesn't. I do that especially with those staying longer as they spend more time in the apartment.
Maybe about a third post a review or send some feedback and I think that's a good rate of return for my purposes.
I think there's no harm in asking and it jogs peoples' memories.