Seeking Advice on Apologizing to Neighbors for My Son’s Noise

Hello r/Japanlife,

This is my first time posting. I need some advice on how to apologize to my neighbors for the noise caused by my son’s footsteps.

I have a 3-year-old son who is very active and energetic. Since February this year, we’ve been living in a fourth-floor apartment. For context, my apartment building has four floors with only three units per floor. Today, we received a letter from the apartment management stating that someone reported noise from a child’s footsteps. We believe it’s our son. I always discipline my son about noise and am very conscious of the disturbance he might cause. We often take him to the nearby park to let him burn off energy, but sometimes he is just too active.

I want to apologize to my neighbors, especially those in the units below us and next to us. How should I go about this? Can I send them a letter and perhaps include a small gift as an apology?

Thank you in advance for your advice.