According to the vocabulary list, Grüße is masculine, but "the greetings" is given as "Die Grüße".
Der Gruß is masculine. Die Grüße is simply the plural.
In German nearly every verb can be used as a noun. It automatically is neuter: "Das Öffnen der Türen während der Fahrt ist strengstens untersagt." In English there appears a gerund. Beware, in German it is not a gerund, the languages use different constructions. "Opening the doors during the ride is prohibited severely."
Yes, you've mistaken the singular with the plural form. But I give you one more: "Das Grüßen" exists as well ;)
How about 'The opening of doors during rides can lead to accidents.'?
Or 'The voting started early in the morning' ?
Does the definite article make all the difference?