A dispute between rival federal worker's unions has snagged efforts to determine when and how government workers should be reimbursed for more than $20 million they paid under a parking fee plan that a federal judge has declared illegal.

U.S. District Court Judge Harold H. Greene told the lawyers yesterday that he would give them one week to come to terms on a settlement or else they would have to argue the legal questions involved before him and let him decide the question of restitution for the federal workers.

Royce C. Lamberth, chief of the criminal division of the U.S. Attorney's for the American Federation of Government Employees (AFGE) and the National Treasury Employees Union (NTEU) refused to sit down in the same room to discuss a proposed settlement of the key element in the parking fee case -- how and when the government should return the fees that were collected at government lots, at a rate of up to $1.8 million a month, from November 1979 to March 1981.

AFGE initially filed the lawsuit seeking to rescind the parking fees, claiming that former President Carter did not have the authority to impose them. NTEU joined as a party to the suit on AFGE's side shortly after the case was filed. Carter imposed the fees for $350,000 federal workers nationalwide, including 75,000 here, in an effort to reduce energy consumption, but Greene ruled that such a plan would first have to be approved by Congress.

Since Green's ruling, NTEU and the government came up with a written agreement to pay back the illegally collected parking fees if the U.S. Court of Appeals eventually upholds Greene's decision. Lawyers for AFGE, however, refused to go along with the proposal, which left Greene with a suggested settlement that is missing the approval of a major party to the lawsuit.

At a brief hearing, Greene said he found it "somewhat surprising" that the unions are "squabbling" with each other over the proposed settlement.

James R. Rosa, AFGE's general counsel, said the problem was "not simply squabbling" but that his union felt the proposed settlement "is a bad deal". Rosa said that while NTEU is willing to postpone reimbursement until the appeals court reviews the case, his union wants the repayment to be made now or at least to have interest paid on the money while the case is pending on appeal.

NTEU's lead lawyer, Robert M. Tobias, contended yesterday that the interest question could be dealt with after the appeals process is complete. Tobias argued in an interview that it is important that the goverment sign a restitution settlement clearing the way for a quick appeal solely on the question of the legality of the parking fee plan.

If the appeals court, reverses Greene's ruling, the reimbursement question would be moot. The government could then seek retroactive parking fees from federal workers for the time since Greene blocked the government from collecting more fees.

Attorneys for both unions, while acknowledging that their organizaions compete for membership in the federal workforce, denied that their argument over the settlement amounts to anything more than a legal dispute.

It is "not a matter of gamesmanship" with NTEU, said AFGE's Rosa, adding "the issue to me is the merits of the case."

Attorney Tobias denied that his union was trying to take over the case from AFGE. "NTEU is not posturing this lawsuit to get an upper hand," Tobias said.