The White House, scurrying to mend its torn relationship with House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), announced yesterday that it had found a high-level White House job for O'Neill's friend Robert Griffin.

Griffin, fired last week as deputy administrator of the scandal-tinged General Service Administration after losing a power strugle with his boss, will join the staff of White House adviser Robert S. Strauss a salary of $50,000.

The speed with which Griffin was placed in a new job - and the cast of characters involved - was a measure of the presidential concern over O'Neill's anger at Griffin's dismissal from the GSA.

Over the past four days, President Carter, Vice President Mondale, Hamilton Jordan, Carter's closet aide, Richard Moe, vice presidential chief of staff and Strauss personally involved themselves in finding work for a bureaucrat most Americans had never heard of until last week.

"I'm quite pleased," Griffin, 61, said yesterday. "I'm terribly grateful."

After Griffin's dismissal last week, O'Neill described himself as "deeply hurt" over the "shabby treatment" he and Griffin had received from the White House. He said chief White House lobbyist Frank Moore had misled him about the fate of Griffin, the speaker's longtime friend and protege from his home state of Massachusetts.

Then, the White House confirmed yesterday, O'Neill barred Moore from the speaker's office and said he would deal only with William Cable, Moore's deputy. White House officials said O'Neill placed his office off-limits to other members of Carter's lobbying team as well - specifically, two aides to Cable.

With Congress already ill-disposed toward many of Carter's legislative programs, administration lobbyists view O'Neill's cooperation as critical and his antagonism as potentially disastrous.

Officials spokesmen for Carter as well as his lobbyists say that, so far, O'Neill has not vented his anger on any Carter bills. O'Neill has also described himself as a "loyal Democrat" who would not seek real retribution against the president.

Yesterday, O'Neill appeared in a conciliatory mood when he said that "time is the curer of all problems. . . I have had four or five conversations with members of the president's Cabinet in the last 36 hours. So the performance between the administration and the speaker's office continues as it has been."

Griffin's job with Strauss is largely undefined. Strauss, a former Democratic National Committee chairman, is currently in charge of trade negotiations and a leader in the fight against inflation. His role in the Carter administration is "continually expanding," presidential spokesman Rex Granum said yesterday, and Griffin "has accumulated a wealth of experience in the federal government" helping to run GSA, the agency that manages all federal buildings.

"I think Bob Strauss is going to use Griffin in a variety of ways," said Moe. He said Strauss had been "talking to us about his additional responsibilities" and the need for more staff.

"There are very few openings at that [Griffin's salary] level. But we discovered this pool of high-level positions that the president can move around," Moe said.