Hi ganr,
To my knowledge, Pinegrow does not have a pubilsh feature in the current version to a remote site. If you install the Atom editor and link it to Pinegrow with the pinegrow plugin and install atom-commander which is a file manger/commander plugin for atom, you can sync your project files to the remote site pretty easily. Just make sure that your index file, once you copied the project, has the correct path’s specified for your assets on the remote server. A common mistake is to move files from a development sandbox server to a remote, but the path’s are not referenced correctly so the site won’t work. Usually on hosted linx servers the path sits within a /www/www directory. Also make sure that your permissions on the remote server are correct for the files in the project. This can usually be set through cpanel or manually with terminal.
If your local website is a wordpress site then it gets a little more complicated because you need to also move the database properly. This is a link to an explanation on the steps, not to reiterate it here.
If you are going to be working on wordpress sites for clients that need to be deployed you might want to look at “DesktopServer” which allows you to manage both local and remote for an annual fee.
Hope this helps.
Vince