This is on the surface is perhaps a surprising move by Everton given the massive controversy and anger that the points deductions have caused this season. But of course there are two recent events that might well explain it.
The first is the fact that the Toffees are safe from relegation regardless after beating Brentford at Goodison Park back on the 28th April.
Then soon after that came the news that Nottingham Forest, who had also been deducted points, had been unsuccessful in their subsequent appeal.
It has been a truly unique and chaotic campaign, one that has been unprecedented in it's adverse impact on the club, team and supporters.
Those deductions totaling ten points and first announced in November, rocked the club and plunged the team back into the relegation fight, which at that point it looked as though the Blues had a good chance of avoiding.
Despite this, Everton managed to pull themselves away from the drop zone and were partially successful in their appeal against the deduction with four points restored to the club.
But meanwhile the Blues were on a dreadful run of thirteen matches without a win that was then compounded by the second two-point deduction then imposed.
With the season in the balance and following a humiliating 6-0 defeat at Chelsea, the Toffees then produced a barnstorming week in which they beat Forest, Liverpool and then Brentford in succession to finally end any lingering threat of relegation.
So, on that basis it doesn't look as though it would make much difference anymore whether or not the club would be successful on appeal.
And with the possibility of a third penalty for further PSR breaches potentially looming, Everton are perhaps also playing a tactical game too.
By dropping this appeal perhaps it might help show a greater willingness to co-operate with the League over this last alleged breach and this could result in leniency in the outcome. We will see.
Another points deduction next season is obviously just about the last thing Everton need after such a traumatic season and with so much uncertainty over the club's future, which is still to be resolved.
At the moment though it seems a legitimate question to ask whether the club will successfully get through a very difficult summer.