MKVToolnix doesn't support remux the output file as the same date as the original input file. This script sets the output file date according to original date of the input file.

RemuxKeepingTheDate.bat

@echo off
cd /d "%~dp0"

:: Unfortunately, MKVToolnix doesn't support remux the output file as the same date as the original input file.
:: This script sets the output file date according to original date of the input file. How does it work? 
:: It works by selecting one or many files and dragging and dropping them onto this script.
:: Coded by PureOcean (2022-04-23+24)
:: Thanks to the commands: https://github.com/gus33000/ESD-Decrypter/blob/master/bin/Rebuild-ISO.ps1#L190=

set "MKVToolNixPath=D:\Program\MKVToolNix"
set "InputFile=%~dpnx1"
set "OutputFile=%~dpn1_remux.mkv"

"%MKVToolNixPath%\MKVmerge.exe" --output "%OutputFile%" ( "%InputFile%" )

ECHO.

powershell -c "$CreationTimeStamp = Get-ChildItem '%InputFile%' | %% {[System.TimeZoneInfo]::ConvertTimeToUtc($_.CreationTimeUtc).ToString('MM/dd/yyyy,HH:mm:ss')}; Set-ItemProperty -Path '%OutputFile%' -Name CreationTimeUtc -Value $CreationTimeStamp; $LastWriteTimeStamp = Get-ChildItem '%InputFile%' | %% {[System.TimeZoneInfo]::ConvertTimeToUtc($_.LastWriteTimeUtc).ToString('MM/dd/yyyy,HH:mm:ss')}; Set-ItemProperty -Path '%OutputFile%' -Name LastWriteTimeUtc -Value $LastWriteTimeStamp;"

ECHO.
pause
exit /b