The template that displays the price in product grids is this one:
skins/customer/items_list/product/parts/common.product-price.twig
First, you should enable the Webmaster mode on the backend page at Look & Feel -> Layout.
Then go to the storefront and navigate to a page that displays a grid of products. Click on the price to make the template selected in the left sidebar (make sure it is customer/items_list/product/parts/common.product-price.twig and not a "child" template, otherwise your changes may affect other pages too).
Click on the template name and alter it to not display the price.
You can find more information on using the Webmaster mode in our knowledge base:
http://devs.x-cart.com/en/webinars_and_video_tutorials/using_webmaster_mode_in_x-cart_5.html