Eviction/Property Removal in Houston

[Joseph West]

In Houston, Texas and have a tenant who does not have a current lease, and agreed to move out due to not being able to pay rent (a full month late).  We never legally filed any eviction, but the tenant did move out 48 hours ago, but has left several things back in the property.  They have date of when they will be able to afford to hire a mover.  The tenant did surrender their keys to me also.  

Am I legally able to move the property to the street and notify the tenant?  When I stated that we may do this to the tenant so we could rent it promptly, I received an email in writing, "I understand."  We want to make sure we cover our *** for the future.  Thanks!