I could feel their worries, and told them that I was only considering single screen-free days. Even that idea left them feeling upset.

1. single 是个普通形容词（“单个的”），可以修饰单数名词，也可以修饰复数名词。网友认为矛盾，可能是觉得它只能修饰单数可数名词吧，其实不然。

2. screen-free：无屏的。为了好理解，直接翻译为：不看手机的。

a single screen-free day  不看手机的一个单日。single 跟 a 或 one 连用，强调“单一”概念，此时可以不用。

single screen-free days （一周或一月内设定）几个不看手机的单日。

3.  我把这几句连起来翻译，以便更透彻理解句意：

I could feel their worries, and told them that I was only considering single screen-free days. Even that idea left them feeling upset.

【翻译】我能感受到他们的担忧，并告诉他们我只是在考虑（提出）几个不看手机的单日。就连这个想法也让他们感到不安。