Hello,  
Do we understand correctly, that you need a report that will email alerts only for PowerShell scripts executed by a Scheduled Task? If you do, find the updated script below:
$taskName = "Inactive User Deleter" # TODO: modify me
$numDays = 1 # set to 0 to output all log records
$operationTypes = @("run script") # TODO: modify me. Values: $NULL or Operation types array 
$to = "recipient@domain.com" # TODO: modify me
$subject = "Actions performed by $taskName" # TODO: modify me
$reportHeader = @"
<b>Actions performed by $taskName during the last $numDays days</b><br/><br/>
<table border="1">
    <tr>
        <th>Start Time</th>
        <th>Completion Time</th>
        <th>Target Object</th>
        <th>Target Object Type</th>
        <th>Operation</th>
        <th>Execution Log</th>
    </tr>
"@ # TODO: modify me
$reportFooter = "<hr /><p><i>Please do not reply to this e-mail, it has been sent to you for notification purposes only.</i></p>" # TODO: modify me
function GetExecutionLog ($logEntryCollection, $executionLog)
{
    $executionLog += "<ul>"
    foreach ($logEntry in $logEntryCollection)
    {
        # Get the operation info
        $type = $logEntry.Type
        $message = $logEntry.Message
        $source = $logEntry.Source
        # Build report entry
        $messageBuilder = ""
        if (-not([System.String]::IsNullOrEmpty($source)))
        {
            # Add source to the message
            $messageBuilder += "$source`: "
        }
        $messageBuilder += "$type - $message"
        # Encode HTML tags
        $messageBuilder = [System.Web.HttpUtility]::HtmlEncode($messageBuilder)
        # Add entry to the report
        $executionLog += "<li>$messageBuilder"
        # Add Execution Log, if any
        $subEntries = $logEntry.SubEntries
        if ($subEntries.Count -ne 0)
        {
            $executionLog = GetExecutionLog $subEntries $executionLog
        }
        $executionLog += "</li>"
    }
    $executionLog += "</ul>"
    return $executionLog
}
# Bind to the directory object representing the General Log
$path = $Context.GetWellKnownContainerPath("ServiceLog")
$serviceLog = $Context.BindToObject($path)
$generalLog = $serviceLog.GeneralLog
# Set start and end dates
if ($numDays -ne 0)
{
   $generalLog.StartDateTime = (Get-Date).AddDays(-$numDays)
   $generalLog.EndDateTime = Get-Date
}
# Get the log records
$log = $generalLog.Log
$records = $log.GetPage(0)
# Add log records to the report
foreach ($record in $records)
{
    if ($record.Initiator.Name -ine $taskName)
    {
        continue
    }
    # Check operation
    if ($operationTypes -ne $NULL)
    {
        $recordOperationTypes = $record.GetOperationTypes()
        $result = Compare-Object -ReferenceObject $recordOperationTypes -DifferenceObject $operationTypes -IncludeEqual -ExcludeDifferent
        if ($result -eq $NULL)
        {
            continue
        }
    }
    if ($record.State -eq "OPERATION_STATE_FAILED_NO_CONTINUE")
    {
        $reportRecord = "<tr bgcolor='red' valign='top'>"
    }
    elseif ($record.State -eq "OPERATION_STATE_FAILED_CAN_CONTINUE")
    {
        $reportRecord = "<tr bgcolor='yellow' valign='top'>"
    }
    else
    {
        $reportRecord = "<tr valign='top'>"
    }
    # Get log record properties
    $recordStartTime = $record.StartTime 
    $recordCompletionTime = $record.CompletionTime
    $recordTargetObjectName = $record.TargetObjectName
    $recordTargetObjectType = $record.TargetObjectType
    $recordDescription = $record.Description
    # Add the Execution Log
    $executionLogEntries = $record.GetExecutionLog()
    if ($executionLogEntries.Count -eq 0)
    {
        $executionLog = "Execution Log is empty"
    }
    else
    {
        # Add execution log to the report
        $executionLog = GetExecutionLog $executionLogEntries ""
    }
    $reportRecord += "<td>$recordStartTime</td><td>$recordCompletionTime</td><td>$recordTargetObjectName</td><td>$recordTargetObjectType</td><td>$recordDescription</td><td>$executionLog</td>"
    $reportRecord += "</tr>"
    # Add record to the report
    $reportHeader += $reportRecord
}
$reportHeader += "</table>"
$messageBody = $reportHeader + $reportFooter
# Send report
$Context.SendMail($to, $subject, $NULL, $messageBody)
If you need a report to email other information, please provide us with as much details per your request as you can.