You may come across an issue where you need to remove a site column from a Site Content Type associated with a list, which of course is not possible using the native GUI (no remove button).

Instead you need to use the Sharepoint Management Shell to remove the offending field.

  1. Logon to the SharePoint Server.
  2. Run Sharepoint Management Shell as Administrator
  3. swap out the following with your information and run it in Sharepoint Management Shell. 
$web = Get-SPWeb http://host.domain/sites/sitename
$list = $web.Lists["List Name Here"]
$field = $list.Fields["Field Name Here"]
$field.AllowDeletion = “true”
$field.Sealed = “false”
$field.Delete()
$list.Update()
$web.Dispose()

If you are having issues, you can try double checking some alternate names of your field using the following: 

$web = Get-SPWeb http://host.domain/sites/sitenamehere
$web.AvailableFields.SchemaXml | Out-File c:\temp\fields.txt

You will be looking for the correlating Field ID of your field name.  For example, if im looking for "Description", id find this string: 

<Field ID="{34A72E09-3CA6-4931-B2E3-F81C40BB87BD}" Name="RoutingRuleDescription" StaticName="RoutingRuleDescription" SourceID="http://schemas.microsoft.com/sharepoint/v3" Group="Document and Record Management Columns" DisplayName="Description" Type="Text" Required="TRUE" CanToggleHidden="TRUE" Sealed="TRUE" MaxLength="255" ShowInDisplayForm="FALSE" Version="3" Description="Provide a description." />