Delete closure from binary cache directory

I maintain a local binary cache for some closures by running nix copy --to file:///cache/dir. However, I couldn’t find a way to delete a closure from the cache.

I tried nix store delete --store file:///cache/dir <path> but got the following error:

error: Garbage collection not supported by store 'file:///cache/dir'

Does anyone know a way to delete a closure from it?