I don’t know if the deck actually poses a problem. Sometimes building jurisdiction approve things that are not suitable. Decks are not known to cause landslides.

However, building jurisdictions have been known to take advantage of a neighbor’s complaint to churn business or put excessive CYA demands on an unsuspecting party. You have to take a wait and see attitude, but be forewarned.

Gather as much info you can, including the feedback that the city gives you on the complaint. Be suspicious of that feedback and any new demands the city might give you. Hopefully , it will turn out to be nothing.