But neither kitten seemed interested and instead they continued to cry out.
Mr Gittings decided to take action and both ended up at the Napier SPCA where they will now wait for a new home.
The animal lover's actions were met with widespread approval after the SPCA posted a photo of "Wilbur" and "Orville" on Facebook.
SPCA Hawke's Bay manager Bruce Wills said the circumstances of the abandonment were "bizarre".
Someone had put the moggies inside a box and then pushed the box into a tip full of discarded cardboard at the depot.
Mr Wills said that usually when people abandoned pets, they left them in a place other people would likely find them.
But this owner had treated the helpless animals as if they were rubbish.
Both kittens were emaciated and crawling with fleas.
Mr Wills said the once timid furry friends were already starting to purr when patted.
"They need a fair bit of TLC before we can allow them to be adopted out," he said.
"They obviously didn't have the best start at life at all."
So far the pair had made it to 500g on the scales but will need to push at least 1kg before they can leave the SPCA.
Kitten season had only just started and with around six months to go, Mr Wills was expecting at least a dozen more arrivals per week.
Temporary foster homes take in many of the kittens before a permanent owner comes along.
There are currently around 50 temporary foster homes but all are full. The SPCA urged people willing to provide assistance to get in touch.
