Writing on the package could be seen through the thick tar-like substance and the product was a Sun Rice brand.
Mrs Bryant's sister found another similar packet the next day.
The Gisborne Herald sent pictures to Sun Rice and a spokeswoman confirmed their products were in two containers on board the container ship, until they went overboard when the Rena split in two early last month.
The thousands of pre-packaged meals from Thailand were en route for New Zealand shelves but are now floating out at sea.
This meant the rice packets took five weeks to float down the eastern coast of the North Island to Gisborne.
Civil Defence emergency manager Richard Steele said as well as the rice, small bags of milk powder and plastic containers had been found washed ashore at Makorori and Wainui beaches.
Yellow foam, which could be insulation from some of the containers on board the Rena, had also been found at Pouawa.
The first sign of debris hit East Coast shores in November. It brought parts of containers, insulation and milk powder to the tip of the Coast around Lottin Point and Hicks Bay.
Gisborne District Council regional on-scene commander Louise Bennett said people would be on the beach tomorrow and Friday to look for more container waste.
United Kingdom-based environmental clean-up specialist company Braemar Howells have the contract for the clean-up from the containers and their contents.
Spokesman Grant Dyson said he was not surprised that debris had turned up.
Bags in particular are obviously very buoyant and can float for a long way. We have a contractor covering the region and there is no question we will step up monitoring and react to more stuff coming ashore if it does. We've had debris over quite a large area of the East Coast off the North Island. It is the nature of the beast.
Mr Dyson said there were 11 monitoring hubs set up from the top of the Coromandel to around the East Cape.
We greatly appreciate being informed of any debris coming ashore from the Rena, so that we can react and tackle it as soon as possible.
People who think they have found something can call 0800 333 771.