How to delete duplicated site columns in SharePoint

I have trouble deleting a duplicated site column in my site collection. The site column in question is the built in HashTags column which is created when the site collection is based on the Project Site template and goes under the Custom Site Columns group.

I have no idea how this column got duplicated. I created a site collection based on Project site template, added some stuff to it, got a backup of it, restored it in another site collection. Then when I tried to add an existing site column to a list, I got the error "no two choices should have the same ID".

After some investigation I realised that there are two HashTags columns in the site collection with the same ID and InternalName. I tried to delete one of them but they appeared to be part of some built in content types. Then I tried to delete it off those content types using some powershell scripts but it does not get deleted. I used the following code:

    $web =Get-SPWeb("http://.......")
    $ct = $web.ContentTypes["Project Policy"]
    $ct.ReadOnly= $false
    $ct.Sealed= $false
    $ct.FieldLinks.Delete("HashTags")
    $ct.Update($true)

But when I go and check the content type in SharePoint Manager, the site column is till part of it.

I would like to know how I can delete this duplicated site column in any way possible.

Regards