Scottish Conservative leader Douglas Ross said there were “serious questions” from Mr Matheson to answer.
He said his party would “seek to get them from the Health Secretary in Parliament this week.”
“But if he has done nothing wrong and has nothing to hide, he will hand over his iPad to prove his version of events,” he added.
Last week, following days of controversy over the whopper of an invoice, Mr Matheson agreed to pay back £10,935.74 incurred in roaming charges during a family holiday in Morocco.
Initially, the SNP minister was only going to pay £3,000 towards the cost from his expenses budget, with the Scottish Parliament agreeing to pay the rest.
However, Mr Matheson, who has an annual salary of £118,511, said on Friday afternoon that he would reimburse the full cost.
The Health Secretary has insisted that none of the bill was down to personal use, and on Monday, the minister suggested that the Scottish Parliament had checked and verified this.
Asked specifically if there was any personal use, Mr Matheson said: “No. As I made very clear on that, when parliament investigated this issue – keep in mind, back in January, where one of their senior IT officials looked into its use as well, then came to a view on this matter, and that’s why an agreement was reached at that particular point.
“Notwithstanding that though, I want to put that question beyond any doubt whatsoever, and that’s why I took the personal decision, as I said in my statement on Friday, that I would reimburse the parliament for the full cost of that, so there’s no questions about what it was used for.”
Asked if he would have over his iPad to allow parliament to investigate, he replied: “They have, they have, they’ve investigated the issue back in January … they had all the data and everything from it. They’ve already had it.”
Asked if parliament had looked through his Ipad, he replied: “They’ve had all that data – they had access to..”
Asked if he had handed over the iPad, the Health Secretary replied: “No, they looked at the iPad, but they had access to all of the data that was on the iPad when they looked at the matter back in January.”
However, a Scottish Parliament spokesperson said: “We can confirm a senior IT official examined Mr Matheson’s iPad in person at Holyrood to ensure it was functioning properly, which was duly established.
“The official reviewed the iPad’s mobile data settings and data use, but the device does not provide a breakdown of data over a specific time-frame.
“The official observed a cumulative total, which accrues over the lifetime of the device.”
Pressed further, the spokesperson told the Telegraph: “We did not look at the browsing history. This would not have showed data volumes consumed. We were primarily looking at volume of mobile data consumed as we had assurances it was for parliamentary purposes.”
Last week, Mr Matheson said the bill was brought about by using “an outdated SIM card in an iPad that I had for constituency purposes.”
He insisted that he was not aware that this had to be replaced, and that ‘the cost built up as a result of that’.
The Scottish Parliament said their records show Mr Matheson was informed by email in February 2021 of the need to change SIM cards from EE to Vodafone.