We suggest that the decay modes of kaons with a pion and a pionium (pi(+)pi(-) atom) in the final state can constitute a not yet considered background to the very rare decay K -> pi nu(nu over bar). In fact, a part of pioniums may escape the decay region before decaying into two pi(0)s (or to pi(0)pi(0)gamma in the case of excited pionium). To illustrate the importance of this background, we show that it may even explain, under some assumptions, the unexpected K_L decay events that appeared in the KOTO experiment.