Curtis has departed for Evo-Stik North rivals Goole because he wants to play regular first-team football.
The attacker has had his options limited in recent weeks, due mainly to the form of Max Wright, Michael Coulson and James Walshaw.
Boss Steve Kittrick said: "He wants to play football, which is understandable.
"Nathan knows the Goole manager Karl Rose and he wants to help him out of the situation they are in.
"We wish him the best, but there is no point in him being at the club if he doesn't want to be here."
Kittrick is happy with the link forged between the club and the Scarborough Football Scholarship, which has seen Josh Wallace, Ben Atkinson and now Chris Pearson sign forms with the first team.
He added: "I spoke to Steve Brennan (Scholarship lead tutor) and asked him to recommend a few players to help us out.
"It is good for the club, good for the scholarship and good for the lads that we have this relationship and they can come through to experience first-team football.
"They will come down on Thursday for the Atherton game and we'll see how things are after that."