You may have been misled by the widespread disinformation campaign that the banking industry is conducting against the new tax withholding system on interest and dividend income.

Big headlines in ads are scaring savers, by saying that "Congress wants a piece of your savings," or that "10 percent of the money you earn in interest is going to disappear."

Those headlines mean only that most Americans owe taxes on their interest income, and the government will be trying harder to collect the legal taxes due. But the ads have frightened many savers, especially the elderly, into thinking that the government is grabbing something extra. Even President Reagan criticized the banking industry last week for the sound and fury of its campaign.

Congress created the new tax-collecting system during its desperate search for revenues last summer, when it became apparent that the budget deficits were getting much worse. An estimated 10 percent of the people who owe taxes on their interest income don't pay--either because they cheat or because they forget. Taxes are also evaded by an estimated 18 percent of the people who earn dividends.

The most efficient way to collect income taxes is to withhold them automatically at the source. That is what's done for the taxes due on wages; they are deducted from every paycheck you get. Automatic tax withholding on pensions and annuities began this year. And starting July 1, there will be automatic withholding on the income you earn from your savings.

Banks, savings and loan associations and credit unions have been trying to repeal this new law. They stacked protest postcards on their counters, and urged their customers to mail them to congressmen and senators. Some of the banks collected signatures and mailed the cards themselves. Some provided stamps. Altogether, they generated more mail on a single issue than most legislators can remember. Cards have been pouring into the Senate Finance Committee at the rate of 30,000 a week.

The banking institutions object to the cost of tax withholding, which will be paid either by their customers (in higher fees) or by their shareholders (in lower profits).

A majority in the Senate and House of Representatives now backs a bill to repeal tax withholding on interest and dividends. But the leadership of both Houses opposes repeal, as does the public official with the biggest vote of all. Reagan announced last week that he would veto the jobs bill if it came to him with a rider repealing interest and dividend withholding. The Senate finally passed the jobs bill Thursday after the withholding amendment's sponsor was persuaded to withdraw in return for its consideration on the floor April 15. The government estimates that automatic tax withholding will pick up an extra $4 billion to $5 billion in taxes next year.

To straighten out the disinformation you have been getting, here is what's scheduled to happen July 1:

* Ten percent of your interest and dividend income will be withheld toward your income taxes due. This is not a new tax. It is simply a new way of collecting the present tax.

* The government is not withholding 10 percent of your total savings, as some people believe. It is withholding 10 percent of the interest earned on your savings which, for most taxpayers, is less than the actual tax due.

* When taxes are withheld monthly from your savings account, you will have a little less money earning compound interest. The banks have been making a great deal of this, claiming that the government is "looting" your savings. But the cost is small. At 9 percent interest, tax withholding will cost you 50 cents a year on each $1,000 in savings. And you need not even lose that. Banks are allowed to withhold taxes all at once, at the end of the year, which would leave all your money free to compound all year.

* All low-income people and most of the elderly can exempt themselves from tax withholding. You are exempt if you paid no more than $600 in federal income taxes last year ($1,000 on a joint return); or if you are 65 or older and paid no more than $1,500 in federal taxes last year ($2,500 on a joint return). The Treasury estimates that 87 percent of the elderly will not be subject to tax withholding.

But to get your exemption, you must file a new withholding form (Form W-6) with the companies that pay you dividends and with each banking institution where you keep interest-paying accounts. That won't be hard. When July 1 rolls around, there will be plenty of information about where those forms can be found