"It's a ridiculous policy...makes me wonder why they chose to eat there?"
Probably, as suggested by Narked, for the free publicity.
Since the policy is longstanding and we are talking about Northern Ireland, it may not be as ridiculous as it first seems. Tattoos may be fashion items now, but that wasn't always the case. The most common ones used to be marks of affiliation to football clubs etc. In Northern Ireland, I'd imagine tattoos could also indicate your political sympathies (Unionist/Nationalist). In that light, asking for tattoos to be covered is akin to asking that patrons do not walk in in football colours (a common request in towns and cities with more than one club) or shouting 'Fuck The Pope' as they come through the door.