Hi,
I tried the ATO>Style Posts & Pages>post container option but it controls only the line below the 'older posts' button. Does anyone know how to delete the one above it?
Many thanks in advance.

I believe the area you're talking about is located in...
ATO--> Next/Previous Navigation --> Style the Navigation Top and or Bottom

In there is a reference for a dashed line. Play with those CSS entries and I think you'll achieve what you're looking for.

Wow! It works, thank you so much!