We're only removing two characters, and we know which two they are. Using Regex seems a bit like overkill in this case. If you were removing a large variation of characters, then I would do a scan to create an index-map of which characters to remove, convert the string into an array, and use a for loop the skips any index in that map (most likely a HashSet<int>) to insert the character's into a string builder to avoid a O(n^2) situation. Yet, if this is only place where you're stripping out characters, then the following code is just fine.
private void button1_Click(object sender, EventArgs e)
{
string s;
try
{
using (StreamReader sr = new StreamReader(sam))
{
s = sr.ReadLine();
}
}
catch
{
s = null;
}
textBox1.Text = s;
if(s != null)
{
s = s.Replace("<", string.Empty);
s = s.Replace(">", string.Empty);
}
textBox2.Text = s;
}