Remove link
Design and Skin Customization
nothing, the place you want to update is index_core_blog_list.tpl
which is in a /module/ directory, so dont touch it because it would be over-written with the next update.
What you want to do is OVER-RIDE that by copying it to your skin and renaming it to jrCore_index_core_blog_list.tpl
Do that and the version in your skin will over-ride the modules version, then any changes you make will be safe through any future updates.
Docs: "Altering a modules template"
https://www.jamroom.net/the-jamroom-network/documentation/module-developer-guide/1051/altering-a-modules-template