All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If your employer (the agency) reimburses you for the money you spent during your travel and asks you for a report (travel expense voucher) in this regard or asks you to determine the expenses, then it is not permissible for you to ask for more than what you actually spent, and you should not include the fees of the hotel while you did not reside there but you stayed with your relative or friend. That is because this is eating up people’s money unjustly and Allaah forbade this as He Says (what means): {And do not consume one another’s wealth unjustly.}[Quran 2:188] Allaah also Says (what means): {O you who have believed, fulfill [all] contracts.}[Quran 5:1]
On the other hand, if your employer gives you a fixed reimbursement for your travel expenses regardless of how much you actually spent, then it is permissible for you to take the whole reimbursement even if you stayed with your relative or any one else. It appears from your question that the company gives you a fixed reimbursement for your travel regardless of the expenses.
However, it is better to refer to the rules of your company and the terms of your contract with your employer because the contract serves as the law of the contracting parties.
Allaah Knows best.