Clearification of a contract signed to a Legal services

Location: Massachusetts

So this is a Legal Contract to represent my mother in her disability case, She was recently granted her disabiliy benefits with backbay to 6 months after her disability started.

She had Used a Legal Service and also gotten Emergency fund for a period of time as well.

She has to pay the Service and the Emergency fund back.

these are the 2 Paragraph in relates to the Legal Representative and the Emergency Fund ( names omitted )

Text between ' ' are the names of the names

" If my Claim is Granted, 'Legal Counsel' will receive twenty-five percent ( 25% ) of the total past-due SSI and/or SSDI benefits payable to or on behalf of me or any of my dependents, or a flat fee of $6,000 if my past-due benefdits exceed $24,000. 'Legal Counsel' has elected to accept a lower representative fee than federal law allows."

"If I owe the state for 'Emergency Fund ' benefits ( ' the non appreviated version of the fund name ' ) which I have agreed to replay, the 'Legal Counsel' fee will be based on 25% of the past-due Benefits remaining after the state is reimbursed for the 'Emergency Fund' benefits or $6,000, whichever is less."

To my understanding of these passages, If her past-due Benefits Exceeds $24,000 she only needs to pay $6,000 to the Legal Counsel , and whichever is lower to the 'Emergency Fund' 25% of the past due or $6,000 of flat fee?

Am I correct on this? The wording is so like round and about but thats what im understanding. I.e. if she had received say $30,000 as her Past Due. she would only need to pay $6,000 to the 'Legal Counsel' and 25% of $30,000 or $6,000 ; whichever is less; in this case $7,500 vs $6,000, back to the 'Emergency Fund'.