List<string> masterList = new List<string>(textBox_masterList.Text.Split(','));
List<string> scrubList = new List<string>(textBox_scrubList.Text.Split(','));
masterList = masterList.Where(x => scrubList.Any(s => x.Contains(s)))
.ToList();
To make search case-insensitive:
masterList = masterList.Where(x => scrubList.Any(s =>
Regex.IsMatch(x, s, RegexOptions.IgnoreCase)))
.ToList();