Lawyer Increasing Rate - No Retainer Agreement

My husband hired a lawyer 2 years ago for a civil matter. The case went to trial.

After receiving the final invoice, he realized that the law firm had increased the hourly rate of the associate on the case 4 times. From 170/hour to 200, then 210 , 250 and the last one 275.

He only realised this after receiving the last invoice because he didn’t properly checked before (he thought he could trusted his lawyer….).

He was never asked about a rate increase, verbally or in written form. (We checked)

Also he didn’t sign a retainer agreement, which we realised is very unusual?

Do we have any recourse? Can we force the law firm to bill us for the initial fee of 170/hour, as they never asked about a rate increase?