When it comes to filtering out unwanted noise or blocking off intrusive conversations, there are several synonyms to replace or enhance the phrase "close your ears to". One such alternative would be "tune out", which implies the ability to selectively ignore or disregard particular sounds. Another choice could be "shut out", as it creates imagery of shutting the door on disruptive noises. Additionally, "ignore" can be used to convey the act of consciously not paying attention to unwelcome sounds or conversations. Lastly, "block off" captures the idea of physically or metaphorically erecting a barrier to prevent the intrusion of sound. All these synonyms offer different nuances while capturing the essence of "closing your ears to" unwanted noise.