Together with the unnamed Nightmare Creature, Grimm gradually disappeared with the arrival of dawn. Each of them went their own lonesome way as daylight fell upon the Nightmare World.
Alas, Grimm had lost the conditions to absorb the other party's Fright Energy so there was no point in giving further chase.
Also, even if he were to wait until nighttime in the Nightmare World, his hunt would most likely end up unfruitful as his prey, fearing for its life, would have long escaped to some other unknown location. Likewise, for the Nightmare Creatures that were previously hot on Grimm's tail, one day alone made all the difference. It would be difficult, if not impossible, for Grimm to sniff out that creature's whereabouts let alone attack it once more.