Many parishes with pews have no kneelers.
Remember, Kneeling does not mean Adoration in the byzantine context, but grief. It gives the implication of being sorrowful for having received communion. Most Byzantines know the Latins mean adoration with it, but when not in Rome…
Where Latinization isn’t rampant, and the priest isn’t on a delatinization kick, it will usually be ignored, or occasionally a Babushka will simply block the kneeler so you can’t put it down. (I’ve seen this done. In two different parishes. By two different babushki.)
If Latinization is rampant, you might be one of several.
If the priest is on a Delatinization kick, you might get a quiet earful after liturgy, or the whole parish might get a quick lesson just before the Royal Doors are closed, reminding that kneeling is a sign of Grief, not Adoration, and therefore inappropriate in a Byzantine Parish after reception of the Holy Eucharist. (I’ve also seen this.)
If Latinization is rampant, and the priest is on a delatinization kick, you might get the lesson as a reminder at the end of the homily… (I’ve also seen this.)
Occasionally, when it’s obvious there are a bunch of Latins present, the reminder not to kneel during the liturgy may be given before the incensation.