Moyes had two spells as West Ham manager, saving them from relegation in his first short stint before leading them into Europe in his second and winning the 2023 UEFA Conference League.
His Everton team are now pushing for European qualification while Nuno Espirito Santo's West Ham are in 17th spot and in the midst of a tense relegation battle.
While Moyes has nothing to prove, the sense that he was not fully appreciated by West Ham's fans might be lurking in the back of his brain as he returns to East London.
With West Ham two points above 18th-placed Tottenham Hotspur, who face bottom club Wolverhampton Wanderers on Saturday, anything other than a win could see them fall back into the bottom three with four games left.
Espirito Santo is well aware of the threat Everton offer and says Moyes's familiarity with the West Ham squad poses a challenge ahead of a vital fixture.
"(Former team) managers have the advantage of knowing the players, sometimes the routines," the Portuguese, who replaced Graham Potter in September, told reporters.
"In this case, David knows the routines, knows the players. So we have to try and make new things happen so we do not become so predictable."
Espirito Santo, who took Nottingham Forest into Europe last season only to be sacked in September, said playing against a former club as a manager is not just another game.
"It is always a special game due to the respect and love that you have from former clubs, but you want to win. You want to compete and win," he said.
West Ham missed the chance to move four points clear of Tottenham when they drew 0-0 at Crystal Palace on Monday but Espirito Santo remains confident that they will stay up, having been seven points adrift of the safety zone in January.
"I think the performance of the team gives us all in the club the hope and the belief that we are competing well," he said.
"All the squad is available, so having all the options to try and help us is very important for us."