Yorkshire's football league teams were informed of the news and how the repayment terms would work on Friday.
The EFL signed a five-year deal with Sky Sports in 2018, which came into effect at the start of this season and the rebate will be deducted from the agreed rights values from the final three years of that deal.
It means the repayments will begin in the 2021-22 campaign but Parry insisted the money to be paid back "is less than half of the minimum rebate amount we initially advised to clubs.”
The football league's broadcast deal with Sky was worth £595m, with Championship clubs set to earn £5m per season while that number was significantly reduced for League One and Two outfits.
It was revealed yesterday that Sky Sports will show 30 of the remaining 108 regular-season games, plus the promotion play-offs, which are currently due to be played in their usual format, with two-legged semi-finals and a final.
All matches, regardless if they are being broadcast by Sky, will be available on each club's iFollow or equivalent streaming service.
Leeds United are likely to feature heavily in Sky Sports' broadcast picks as they push for promotion while Huddersfield, Middlesbrough, Hull and Barnsley will be seen by a national audience in their respective bids to beat the drop.
EFL clubs are due to discuss the new rebate agreement with Sky Sports on Wednesday.