Translation:I forgot my towel in the bathroom.
The two sentences have similar but not identical structure. So I'm not that the correctness of one shows the correctness of the other.
In "forgesi hejme la gantojn". You have the adverb "hejme"
In "Mi forgesis mian bantukon en la banĉambro." You have phrase "en la banĉambro".
They both describe the verb "forgesi" but "en la banĉambro" seems a lot more explicit since it specifies in the bathroom. However "hejme" seems less explicit as it's just an adverb derived from "hejmo" but it doesn't include any more information.
Despite saying that, I will admit that PIV defines "hejme" as "En sia hejmo".