This can be done in three steps:
// 1. Read the content of the file
string[] readText = File.ReadAllLines(path);
// 2. Empty the file
File.WriteAllText(path, String.Empty);
// 3. Fill up again, but without the deleted line
using (StreamWriter writer = new StreamWriter(path))
{
foreach (string s in readText)
{
if (!s.Equals(lineToBeRemoved))
{
writer.WriteLine(s);
}
}
}