Make a duplicate of the card. Change the fill to solid and the outline to none.
The duplicate will be on top. Make sure that the duplicate is center-aligned with the original card.

Select the blended lines, and then the duplicate card (hold down the Shift key to multiple-select) and from the Arrange menu, select Combine Shapes > Intersect Shapes . The duplicate card goes bye bye and the blended lines have been trimmed to fit the card shape.

Select the lines, eye symbol and card and group them (Ctrl-G)