The Wirral Globe reported that staff called police to the pub on Monday at 6.30am when they discovered thieved had broken in, caused damage and stolen cash.
Rimmer opened the pub, his second venture in the pub trade for his company Flying Pig & Lobster last week.
Rimmer runs the company with Revolution Bars co-founder Roy Ellis and already owns the Elephant in Woolton Village, Liverpool.
Rimmer previously told the Publican's Morning Advertiser’s sister magazine MCA they were eager to see if the concept, which they said was in the mould of Brunning & Price, could be significantly grown.
He said: “Could you have a few hundred of these? Of course you could. The opportunity is massive. But for now, our idea is to add two or three a year and enjoy it and build fantastic pubs that we love.”
Rimmer was embroiled in minor controversy earlier this year when the TV show he presented, Tricks of the Restaurant Trade, came under fire from the industry for claims it made about whether it was safe to serve rare and medium-rare burgers.
The British Hospitality Association (BHA) at the time said while coking rare burgers could be unsafe if done in uncontrolled conditions, the show focused only on the burgers’ colour rather than what businesses were doing to ensure food safety.