Log into the GenesisNX web GUI by typing its IP address in any web browser that is on the same network as the GenesisNX.
Navigate to "Configuration->Nas Resources->Shares". Under "Create new share" choose "Specified path:" and choose the share in which the file you wish to delete is located.
Double click on the share and naviagte to the file you wish to delete. Choose the file and click on "delete". Be aware there is no restore option or recycle bin, so this will be a permanent delete.