Based on the solution and awesome breakdown for matching patterns inside wrapping patterns you could try:
\[\{\#(?<Text>(?:(?!\#\}\]).)*)\#\}\]
Where \[\{\# is your escaped opening sequence of [{# and \#\}\] is the escaped closing sequence of #}].
Your inner values are in the matching group named Text.
string strRegex = @"\[\{\#(?<Text>(?:(?!\#\}\]).)*)\#\}\]";
Regex myRegex = new Regex(strRegex, RegexOptions.IgnoreCase | RegexOptions.Multiline | RegexOptions.Singleline);
string strTargetString = @"Employee name is [{#John#}], works for [{#ABC Bank#}], [{#Houston#}]";
foreach (Match myMatch in myRegex.Matches(strTargetString))
{
  if (myMatch.Success)
  {
    var text = myMatch.Groups["Text"].Value;
    // TODO: Do something with it.
  }
}