There is no issue with the template. Those lines are appearing because of the lines that are present throughout the transparent areas.
These lines appear because the image gets slightly compressed when the algorithm puts the template on the shirt.
A solution is to create two layers in your drawing program: One for the template and one (or more) for the shirt. The template layer should always be on top. When you draw the shirt, use a layer lower than the template.
When you’re complete, hide the layer with the template and then export.
From this:
To this:
