As far as I know, veneration of a icon that is a forgery is equally authentic as it speaks to the heartmind of the venerator rather than the veneration.
At the same time, there is a level of “what is reasonable” too. During my convert-itis phase in my late 20s as Uber-Orthodox Christian, I had a noisy argument with a Russian priest at throwing out the church bulletins which had an icon on the front.
I lectured him, a 70+ year old priest, his wife trying _not_ to roll her eyes, but I could see it, on the nature of veneration, quoting some Desert Fathers.
He patiently listened, smiled politely, nodding his head at appropriate times.
Then he blessed me and walked off.