You could clear the show legend checkbox on Properties | Dimension. That would suppress the display on all the charts.
If you want a scale on one chart only you might want to overlay a filtered chart with the x axis legend displayed. Use Shft-Crtl click to drag the display part of this chart and resize the object so that only the legend displays with a transparent background to the same size as the trellis charts. If the now invisible expression is the same as one of the legend charts, it will rescale the same when selections are made. This does assume that the trellis charts all have the same x-axis range.
Logic will get you from a to b. Imagination will take you everywhere. - A Einstein
There was something with that, just not sure what it was anymore. If I find out I will let you know, in the meantime I've copied the trellis chart from the trellis document on the community to your document and changed it to your chart settings.