The federal officials who regulate savings and loans could take unlimited amounts of money from "industry trade groups" as reimbursement for travel and related expenses, under a provision in the comprehensive banking bill introduced yesterday by Senate Banking Committee Chairman Jake Garn (R-Utah).

The measure, which comes at a time when the regulators are under fire for being too closely tied to industry, does not stipulate that such payments be made public. However, aides to Sen. Garn insisted yesterday that a promise of dislosure would be required before Congress would allow officials at the Federal Home Loan Bank Board to receive payments "in cash or in kind."

The bill leaves to the bank board, the federal agency that regulates S&Ls, the right to set a ceiling on the amount of reimbursement.

The bank board requested the reimbursement provision in a letter signed by its chairman, Edwin J. Gray, to Garn, congressional banking committee aides said. Garn included the provision in the banking bill he unveiled yesterday.

The reimbursement provision would exempt bank board employes from a 1965 presidential order that bars such payments to government employes because it "might result in, or create the appearance of . . . using public office for private gain; . . . giving preferential treatment to any organization or person; . . . losing complete independence or impartiality of action; . . . or affecting adversely the confidence of the public in the integrity of the Government."

House and Senate banking aides said that the bank board has compared the reimbursement policy to one now used by officials of the Securities and Exchange Commission. The purpose of such reimbursement provisions is to get around government expense-account limitations that many federal employes say are too low.

Daily expense allowances vary according to where a government employe travels, but the maximum amount permitted is $75 a day. Under newly proposed rules by the General Services Administration, the limit will go as high as $126 a day starting next month.

SEC rules require that officials who are reimbursed by industry keep detailed records of such payments and make them public.

The bank board "possibly" would adopt disclosure rules, but cannot unless Congress passes the reimbursement law, said the bank board's acting chief lawyer, Harry W. Quillian. Until then, he said, "There is no reason to enact such regulations. We'd be spinning our wheels."

Officials within industry and government have said that the bank board does not regulate the thrift industry as well as it might because it is too influenced by trade groups or various sectors of the industry.