There's a message on their contact us page:
"....We are aware of the claims made this morning regarding the security of customer data within our Apps. We can assure our customers that all password and payment information is and has always been safe. The security of your shopping experience at Moonpig is extremely important to us and we are investigating the detail behind today’s report as a priority. As a precaution, our Apps will be unavailable for a time whilst we conduct these investigations and we will work to resume a normal service as soon as possible. The desktop and mobile websites are unaffected..."