Over the past few years, banks have systematically raised their old fees and invented new ones that are harder and harder for consumers to avoid.
(A) banks have systematically raised their old fees and invented new ones that are harder and harder for consumers to avoid - has no error. Hence, (A) is the right answer choice.
(B) banks are systematically raising their old fees and inventing new ones that become harder and harder for consumers to avoid. - the non-underlined phrase ''Over the past few years'' is the equivalent of the present perfect tense since it is used to indicate an event that began in the past and whose effect is still felt today. In such a setting, you cannot use the present continuous tense ''are..raising''.
(C) banks systematically raising and inventing new ones make them harder and harder for consumers to avoid - ''Over the past few years'' is the equivalent of the present perfect tense since it is used to indicate an event that began in the past and whose effect is still felt today. In such a setting, you cannot use the present continuous tense ''raising and inventing''.
(D) as banks systematically raised their old fees and invented new ones, avoiding them becomes harder and harder for consumers - the demonstrative pronoun ''them'' has several possible antecedents: fees, banks, years.
(E) as banks have systematically raised their old fees and invented new ones, it is becoming harder and harder for consumers to avoid them. - the demonstrative pronoun ''them'' has several possible antecedents: fees, banks, years.