First, depending on the agreement when you embarked on the business travel, they might not have any claim for recovery of the travel expenses at all--that is, if at the time you went on the travel, they were supposed to reimburse your expenses and there was no agreement that if you quit they could recover those expenses, then they cannot recover them. The company must honor the agreement or policy in place at the time in regards to expenses, and only if that agreement or policy had been to require repayment if you quit would they have a claim for the money.Second, even if they had a valid claim to recover the expenses from you, they could not deduct it from your wages without your agreement or consent. The law does not allow wage deductions without employee agreement (other than those, like certain taxes, required by law). If they think you owe them money and you will not  repay it, their recourse is to sue you for the money.