Sky king (my pilot buddy i shoot with) told me horizonal strings are often a trigger control issue, he says dont let trigger finger touch wood or fiberglass only the trigger. Try it out and let me know if it worked it helped me . ebb
stock pressure= you may be pulling down hard enough that the fore end contacts the barrel on some shots and not others. also you may have parallax and if you change the position of your shoulder or face that could cause the horizontal string.--if non of these or the other things work out i would send the scope back or at least call them and see if they have ever had this problem--if nothing else try it on a rifle of known accuracy and try to shoot a square by clicking the scope.