Both servers have SQL 2008 R2 SP3 installed. HOWEVER,
No, I'm afraid not. You say that the source server is 10.50.6550, which means SQL server 2008 R2. But the destination server is 9.0.4035, which is SQL Server 2005. And you cannot restore a backup on a lower version of SQL Server. There is no way around that.
So either you get yourself a newer version of SQL Server on the destination server or a differens means to get the data from the source to the destination server. Considering that these SQL Server has been out of support for a while, you might want to take this to a higher level and consider whether your environment in general should be on something which is supported.
SQL Server version list: https://buildnumbers.wordpress.com/sqlserver/