Ministers are required to respond to the petition after it reached 1,000 signatures.
A total of 5,000 signatures could trigger a debate in the States.
Jean McDonald, an animal charity worker who lodged the petition, said the increased costs would “only cause more worry”.
She wrote: “We run a self-funded rescue animal charity and paying 5% more on Amazon and eBay orders will add to our costs and is wrong.”
Under the new rules, big retailers such as Amazon collect the GST when an order is placed.
Government guidance for overseas retailers suggests the current threshold of £60 “will eventually be removed altogether”.
Deputy Ian Gorst, the treasury and resources minister, said last month charging GST on offshore retailers was an issue of fairness.
He said islanders already paid 5% tax on items bought from domestic retailers.
He said: “It cannot be right, for example, that a £25 item bought in our high street is taxed, while the same item from a large offshore retailer is supplied tax-free.”