I feel it is most likely that they are talking about what is commonly known in American English as the "security deposit"--the extra amount paid by the renter before beginning a rental to cover damages, unpaid rent, etc. If the renter does not miss any payments or damage anything, he gets his security deposit back.

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Note added at 5 hrs (2018-02-12 03:27:55 GMT)
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http://www.courts.ca.gov/1049.htm

I think "authorise" is better than "grant" here.