Removing square brackets from column headers DAX query

Confirmed your test, the square brackets are not present in DAX Studio when running the same query. The full PowerShell script is below and is ran in PowerShell 7.

[System.Reflection.Assembly]::LoadWithPartialName("Microsoft.AnalysisServices.AdomdClient") 

$PowerBIEndpoint = "REDACTED"
$PowerBILogin = ""
$PowerBIPassword = ""

$Query = 
"EVALUATE
    SUMMARIZECOLUMNS (
        'XactlyTemplate'[Performance Month],
        'XactlyTemplate'[Invoice Number1],
        'XactlyTemplate'[Transaction Date],
        'XactlyTemplate'[Customer Unique ID],
        'XactlyTemplate'[Customer Name],
        'XactlyTemplate'[Customer State],
        'XactlyTemplate'[Customer Region],
        'XactlyTemplate'[ContractID],
        'XactlyTemplate'[Contract Start Date],
        'XactlyTemplate'[Contract End Date],
        'XactlyTemplate'[Order/Contract Term in Months],
        'XactlyTemplate'[Order/Contract Term in Days],
        'XactlyTemplate'[Usage Type],
        'XactlyTemplate'[AcctAssignGroup],
        'XactlyTemplate'[Revenue Type],
        'XactlyTemplate'[Transaction Type Description],
        'XactlyTemplate'[Stock_Material Code],
        'XactlyTemplate'[Stock_Material Code Description],
        'XactlyTemplate'[Product Name],
        'XactlyTemplate'[Sub-Product],
        'XactlyTemplate'[Recurring/Non-Recurring],
        'XactlyTemplate'[Currency],
        'XactlyTemplate'[Sales Org],
        'XactlyTemplate'[Business Unit],
        'XactlyTemplate'[Partner Account],
        'XactlyTemplate'[Partner Name],
        'XactlyTemplate'[Sales Team],
        'XactlyTemplate'[Employee_ID_2],
        'XactlyTemplate'[Employee_2_Split_Percentage],
        'XactlyTemplate'[Employee_ID_3],
        'XactlyTemplate'[Employee_3_Split_Percentage],
        'XactlyTemplate'[Employee_ID_4],
        'XactlyTemplate'[Employee_4_Split_Percentage],
        'XactlyTemplate'[Employee_ID_5],
        'XactlyTemplate'[Employee_5_Split_Percentage],
        'XactlyTemplate'[Employee_ID_6],
        'XactlyTemplate'[Employee_6_Split_Percentage],
        'XactlyTemplate'[Employee_ID_7],
        'XactlyTemplate'[Employee_7_Split_Percentage],
        'XactlyTemplate'[Employee_ID_8],
        'XactlyTemplate'[Employee_8_Split_Percentage],
        'XactlyTemplate'[Employee_ID_9],
        'XactlyTemplate'[Employee_9_Split_Percentage],
        'XactlyTemplate'[Employee_ID_10],
        'XactlyTemplate'[Employee_10_Split_Percentage],
        'XactlyTemplate'[Employee_ID_1],
        TREATAS ( { DATE ( 2020, 9, 1 ) }, 'XactlyTemplate'[Performance Month] ),
        `"No_of_Units`", CALCULATE ( SUM ( 'XactlyTemplate'[# of Units] ) ),
        `"Total_Amt`", CALCULATE ( SUM ( 'XactlyTemplate'[Total Amt] ) ),
        `"Employee_1_Split_Percentage`", CALCULATE ( SUM ( 'XactlyTemplate'[Employee_1_Split_Percentage] ) )
)"

$ExportPath = "REDACTED\Export.csv"
  
$Connection = New-Object -TypeName System.Data.OleDb.OleDbConnection
$Results = New-Object System.Data.DataTable
$Connection.ConnectionString = "Provider=MSOLAP.8;Data Source="+ $PowerBIEndpoint +";UID="+ $PowerBILogin +";PWD="+ $PowerBIPassword  
$Connection.Open() 
$Adapter = New-Object -TypeName System.Data.OleDb.OleDbDataAdapter $Query ,$Connection
$Adapter.Fill($Results) 
$Results | export-csv -Path $ExportPath -NoTypeInformation -Encoding UTF8noBOM
$Connection.Dispose()
$Connection.Close()

SOURCE: https://sqlitybi.com/how-to-export-data-from-power-bi-using-xmla-endpoints/