The CRA may apply your GST/HST credit against certain outstanding federal, provincial, or territorial government debts. These may include student loans, Employment Insurance and social assistance benefit overpayments, Immigration loans, and training allowance overpayments. They may also apply it to satisfy a garnishment order under the Family Orders and Agreements Enforcement Assistance Act.
It really doesn't matter who claims the GST/HST credit, as long as only one member of a household claims it. It is a tax-free payment to help lower income individuals and families offset the cost of the GST/HST. It is based on the number of children you have and on your net family income (not including that of your children).
GST/HST credit payments are not considered income. You do not have to report them on next year's return.