I think this will do it:
$mysiteHostUrl = "https://mysites.mylrh.org"
$mysite = Get-SPSite $mysiteHostUrl
$context = [Microsoft.Office.Server.ServerContext]::GetContext($mysite)
$upm = New-Object Microsoft.Office.Server.UserProfiles.UserProfileManager($context)
$AllProfiles = $upm.GetEnumerator()
foreach($profile in $AllProfiles) {
if($profile.PersonalSite -ne $Null) {
$site = new-object Microsoft.SharePoint.SPSite($profile.PersonalURL.AbsoluteUri)
$site.SecondaryContact = $null
write-host $profile.DisplayName "personal site re-permissioned successfully"
}
}
$mysite.Dispose()