But considering he still had another couple of years of his deal to run, it also surprised a few more.
Not least because there are a clutch of important team-mates - Joe Ledley, Georgios Samaras and Anthony Stokes - who are now in the final year of their contracts.
It was not a case of Efe jumping the queue. It must have suited both club and player to get that bit of business done now.
However, there is an increasing need for Celtic to try and do the same with these others because, while we speak about their contracts being up next summer, what we should really be focusing on is January.
That's when they can start talking to other clubs and can sign pre-contract agreements.
That day dawns less than three months from now, so the sooner they are secured on new contracts, the easier everyone can breathe.
The break for internationals can often afford a manager or chief executive the opportunity to sit down with such players and talk about what they want and what is available.
But when you are dealing with guys who are representing their countries, not only are they not here, but while they are away there is talking done between them and international team-mates who are often only too willing to tell them how much more money they are on at their clubs.
I know that was the case when I was playing for Scotland and heard how much the Anglos in the squad were making. The fallout from that can be difficult to manage.
Which is why I would advocate speeding up negotiations, which I am sure have already begun.
Anthony has already made it public he wants his future settled, and that there remains a gap between what he is looking for and what the club are offering.
His hand is strengthened by the fact he is enjoying a good start to the season and has even got himself back into the Republic of Ireland squad.
Joe is another who has been speaking to the club for some time about a new contract, and has made it clear he would like to extend his stay.
Due to the fact he arrived here from Cardiff City on a Bosman, when there was quite a bit of competition for his signature, Celtic would have put him in at the top end of their wage scale.
Can he expect the same to be offered now? Well, he has been struggling to shake off a persistent hip problem, but Neil has never tried to hide what an important member of the team he is, and there is no doubt he still has a lot to offer.
For me, though, the man who I believe Celtic and Neil must make the priority is Georgios.
A few years ago, I never thought I would hear myself say that. But he is now such a key player for the club, especially in the big games.
Georgios took a big pay-cut to sign from Manchester City, and has had opportunities to leave - presumably for more money - since then.
His profile has risen greatly with his performances against top clubs in the Champions League. Even the Barcelona fans have made it known they would like him to be signed.
And he is a big, big player for Greece, who are challenging to qualify for next summer's World Cup finals.
But Georgios has always insisted he has no desire to play for anyone else, and it is a fact some players are very content with their lot when they find a club and an environment that really suits them and their family.
However, you can't rely on this always remaining the case and the quicker the club sit down with Georgios and his representatives and agree the terms the better.
Of course, there are always occasions when, no matter what you offer a player, he will say no because he believes moving on is right for him at that stage of his career.
Gary Hooper was a case in point, and the fact he was in the final year of his contract when he left in the summer was reflected in the transfer fee Celtic got for him.
It's also true that, if a player is playing particularly well, no matter what stage of his contract he is at, the offer that comes in might make it too hard to stand in the way.
It happened with Victor Wanyama, and it might be the case with Fraser Forster.