This Powershell script will let you remove a specific User Profile property without having to use Central Administration. This can be handy in a few different scenarios.
Script is:
Add-PsSnapin Microsoft.SharePoint.PowerShell -ErrorAction SilentlyContinue
$site = Get-SPSite "http://somesharepointsite.com"
$context = Get-SPServiceContext($site)
$upcm = New-Object Microsoft.Office.Server.UserProfiles.UserProfileConfigManager($context)
$cm = $upcm.ConnectionManager
$pdtc = $upcm.GetPropertyDataTypes()
$ppm = $upcm.ProfilePropertyManager
$cpm = $ppm.GetCoreProperties()
$ptpm = $ppm.GetProfileTypeProperties([Microsoft.Office.Server.UserProfiles.ProfileType]::User)
$psm = [Microsoft.Office.Server.UserProfiles.ProfileSubTypeManager]::Get($context)
$ps = $psm.GetProfileSubtype([Microsoft.Office.Server.UserProfiles.ProfileSubtypeManager]::GetDefaultProfileName([Microsoft.Office.Server.UserProfiles.ProfileType]::User))
$pspm = $ps.Properties
# Remove User Profile Property by Name
$cpm.RemovePropertyByName("NAMEOFPROPERTYTODELETE")