Sentence:  [T]hey prayed me to be their Surety for payment of their Ranſom-Money; and herein every one was very forward with his Pretences; one alledged Nobleneſs of Birth; another, that he had great Friends and Alliances; a Third, that he was a Commander in the Army, and had much Pay due to him; a Fourth, that he had Caſh enough at Home, and was able to <WSD>imburſe</WSD> me. 
Meaning of the word marked with <WSD> tags:  To pay back money that is owed; to refund, to repay, to reimburse.