They said there were clear signs on the skip saying it was private. Its contents were later set on fire.
Derek Wells said he and his brother, who did not want to be named, arrived from overseas after their brother, Peter, was killed when the bicycle he was riding and an empty logging truck were in a collision on State Highway 1 near Anzac Ave on November 15.
The brothers were staying at Peter's home in Great King St, which they are clearing out.
Mr Wells said, soon after he hired a skip on Friday, someone tried to put rubbish in it, believing it was a free skip routinely provided by the city council at the end of the student year for rubbish.
So the brothers put up multiple signs saying it was privately paid-for, asking people not to dump their rubbish there.
On Saturday, it was nearly empty when the men left for their brother's funeral, but when they returned it was three-quarters full, a shopping trolley part of its contents.
Mr Wells said, when he asked three young men not to put more stuff into the skip, they told him they could do what they wanted.
"Their attitude was 'so what?' They basically said, 'What's your problem?"'
Even after the brothers explained their situation, at least one of the group continued to argue they had a right to dump their stuff in the skip, Mr Wells said.
Then, at 1.30am yesterday, he was woken by noises outside the house, to find the Fire Service extinguishing a fire in the skip.
"We had just been tidying up the house, trying to deal with the arrangements for the funeral, trying to keep ourselves busy, really. I know they could not have known that, but this attitude, it just leaves a real bad taste in your mouth."
They were also left out of pocket because they had paid $225 for the skip, now nearly full, and they would have to get another.
Everyone else - from the police and St John to the funeral director and his team - had been "absolutely wonderful", Mr Wells said.
"This is just disappointing after the compassion and kindness everybody else has shown, and then to be confronted by these [people] ... I don't think I can use words you could print to describe them."
The brothers did not report the incident to police.