You can use the str accessor to get string functionality. The get method can grab a given index of the string.
df[~df.col.str.get(0).isin(['t', 'c'])]
col
1 mext1
3 okl1
Looks like you can use startswith as well with a tuple (and not a list) of the values you want to exclude.
df[~df.col.str.startswith(('t', 'c'))]