絆された is read ほだされた and means being emotionally tied down or won over by someone's kindness and affection. In the song, the narrator remains "絆されたまま" in a dream, suggesting they are unable to break free from the tender memories and feelings connecting them to someone.
"Grace Note" opens on a notebook: 開いたノートに綴った青さは (the blueness I wrote into an open notebook). That 青さ (aoi-sa, literally "blueness") is the Japanese way of saying youthful, unripe feeling, so picture a school kid scribbling feelings they can't name yet, then scanning the crowd for someone's back when the final bell rings: 終わりのチャイムに君の背中を探してた (at the closing chime, I was searching for your back). The title makes sense from there. A grace note is a tiny ornamental note in music, and the singer keeps describing a sound that won't fit on paper: 譜面にできない音色 (a tone that can't be written as a score).
The chorus is the part that sticks. 生まれたときは ひとりぼっちだったこと (that when we were born, we were all alone) is something she worries we forget, and by the end it turns gentle: みんな同じなんだよね (we're all the same, aren't we). Watch the little ending かな (kana, "I wonder"), which turns up again and again, as in どの言葉で歌にできるかな? (with which words could I turn it into a song?). Learning that one particle gets you most of this song's shy, questioning mood. There's also a lovely image of a pale butterfly landing on a finger, ふわり指に止まった淡い蝶 (a pale butterfly softly landed on my finger), where ふわり is a sound-word for something light and floating.