By looking for Katarina Rostova in Season 6, he is basically telling her, that has resulted in the danger that she now faces from this organization called the Townsend Directive that is looking for Katarina and will do anything and hurt anyone who stands in their way.
All of a sudden, now, she realizes not only does her connection to Red still haunt her and potentially cause danger for her daughter, but Red points out, and I think this is what you meant by the tension, that it’s Liz’s fault for going out and doing the one thing Red asked her not to do, which was look for Katarina Rostova.