How do you replace all the occurrences of a certain character in a string?

The problem is you're not doing anything with the result of replace. In Python strings are immutable so anything that manipulates a string returns a new string instead of modifying the original string.

line[8] = line[8].replace(letter, "")

I would use the translate method without translation table. It deletes the letters in second argument in recent Python versions.

def remove_chars(line):
    line7=line[7].translate(None,'abcd')
    return line[:7]+[line7]+line[8:]

line= ['ad','da','sdf','asd',
        '3424','342sfas','asdfaf','sdfa',
        'afase']
print line[7]
line = remove_chars(line)
print line[7]