How to remove the ASM TS* Cookie

HTTP_REQUEST_RELEASE is fired just before the Request from the Client is being sent to the Server-side (pool member), so my understanding is that is not what you want. You want the opposite - you want ASM to stop sending TS cookies to your client, you need to use HTTP_RESPONSE_RELEASE event,e.g:

  HTTP_RESPONSE_RELEASE    {
  set cookies [HTTP::cookie names]
  foreach aCookie $cookies {
    if {$aCookie matches_regex {^TS(?:[0-9a-fA-F]{6,8})(?:$|_[0-9]+$)}} {
       Remove ASM Cookies
      log local0. $aCookie
      HTTP::cookie remove $aCookie
    }
  }
}

I am not quite sure about the version of BIG-IP you are using, I reported a bug in HTTP::cookie remove functionality to F5 years ago, it is likely that this will work only from version 11.6.1/12.0, a workaround was to use HTTP::header remove instead of cookie remove.