Senate Finance Committee members indicated yesterday that they want to amend the Reagan administration's proposed tuition tax credit to cut its cost from $1.25 billion to $900 million over the next three years.

No votes were taken on the bill, but Chairman Robert J. Dole (R-Kan.) and several other members made it clear that amendments would be offered in three areas:

* Adding a "refundability" clause so that poor families who owe no taxes could take advantage of the credit. If a family's credit was greater than its tax liability, the Treasury would send it a check for the difference. Sen. Bob Packwood (R-Ore.), longtime tuition tax credit supporter, said that at least three absent senators also favored this idea, which would add $50 million to the bill's cost and make it less susceptible to the charge that it would mainly aid the rich.

* Reducing the maximum tax credit to $300 per child, rather than $500.

* Phasing out the credit at lower income levels than the administration bill, which would start reducing it when a family's income reached $50,000 and deny it for those with incomes over $75,000. Dole said he would make these figures $40,000 and $60,000.

Dole said that the three amendments would lower the bill's cost to $900 million.

As the meeting started, Dole read a letter from President Reagan reiterating his hope that the bill will be enacted this session of Congress, which is scheduled to adjourn in October. Others doubt this will happen.

Packwood sought assurances from administration officials at the mark-up that the anti-discrimination provisions in the bill are "iron clad and wiggle proof." He said, "I cannot emphasize how critical it is to this administration to have no odor of discrimination in this bill."

The administration was severely criticized by civil rights leaders earlier this year for changing its position in a Supreme Court case and saying that the Internal Revenue Service didn't have the authority to deny tax exemptions to private schools that discriminate.

John E. (Buck) Chapoton, assistant secretary for tax policy at the Treasury Department, said that the administration was sensitive to the civil rights concerns. But he said that it would oppose adding "refundabilty" to the bill because it was controversial and violated tax policy principles.

He also opposed lowering the eligibility income cap much below the administration proposal on the grounds that the bill then wouldn't help very many people.

The bill has been attacked by most public education groups as unconstitutional and potentially harmful to public schools. It also has been opposed by fiscal conservatives as too expensive at a time of huge federal deficits.

Sen. Harry F. Byrd Jr. (Ind.-Va.) said at the hearing that he had seen too many government programs start out small and then "mushroom."

Sen. John C. Danforth (R-Mo.) said that he supported the concept of tuition tax credits but wanted to know, "How am I going to answer the question, 'How can you vote to cut Pell grants or guaranteed student loans . . . and then put in place a new, what amounts to, a new entitlement program?' "

Chapoton said that the administration considered the tuition tax credit a "special case." Danforth said after the hearing that he would have "to ponder" whether that was a satisfactory answer.