Lighting artifacts through transparent material

I've been having an issue for a while now in Unity, where light is creating grid-like shadow artifacts when it passes through a transparent texture.

The materials in question are using the Standard shader, and any edits of it don't seem to make a difference. The Legacy Transparent Specular shader doesn't cause these artifacts, but I'd like to avoid it if possible. Is there any simple fix for an issue like this? I haven't managed to find anyone else with the same problem...