The Sydney sailing club that refused entry to global celebrity Pink in an ID crackdown has invited her for “a ride on one of our skiffs”, as it tries to make up for the incident.

The Manly Skiff Club spoke out again on Thursday, after it emerged it had refused the superstar entry earlier this week because she could not produce photo identification.

“I overheard her saying that she had a booking, but when they asked her to provide her ID, she said she didn’t have any on her,” Manly Market manager Mark Eymes told the Manly Observer about Monday’s incident.

“They said she couldn’t come in without it, even though she explained that she’d already secured her booking with a deposit.”

Under NSW’s strict rules for registered clubs, locals must be members to enter. Visitors from out of town have to produce photo ID when they sign in.

Pink, who is in Australia for her Summer Carnival Tour, and her accompanying group of eight were all turned away.

“Next thing, I saw Pink and her group walking away. They just turfed her out,” Eymes said.

Manly Skiff Club secretary manager Matt Hazell had already apologised. But on Thursday afternoon he went further, saying club staff were just following the rules and the singer wasn’t “turfed out”.

“But let’s be honest, we were disappointed at how things played out, and we’re sorry Pink and her team couldn’t enjoy our signature Skiff Club hospitality,” he told The Sydney Morning Herald.

“Pink, we’d love to have you back to ‘raise a glass’ and show you the best of Sydney Harbour. We could even take you for a sail on one of our skiffs.”

Hazell apologised again to the singer for any embarrassment due to the incident. He said the club had missed “a real opportunity” to host her.

“It’s important to clarify that Pink was not ‘turfed out’; she chose to leave after encountering the sign-in process issue,” he said.

Sadly for the club, Pink is unlikely to take up its offer anytime soon. She and husband Carey Hart were reportedly seen at Sydney Airport on Thursday, with 12-year-old daughter Willow and seven-year-old son Jameson in tow. They were boarding a plane for Queensland, as Pink’s Summer Carnival tour continues.

The family has been sighted out and about in Sydney numerous times in recent days, including at Circular Quay and Bondi.

Pink performs in Brisbane on Friday and Saturday, and the Gold Coast on Tuesday. After that her tour heads to Melbourne, Adelaide and Perth.