More than likely, as he was not the resident there, they could not get a warrant due to lack of proabable cause or they surely would have one.
If for some strange reason they did not seek one and went there asking for a concent search, they should leave a squad of agents there to ensure nothing comes or goes and come back with one post haste now. More than likely there is something there the parents do not want found probably over civil suit considerations thanks to our litigious society.
The FBI needs access to a lot of information in order to support the Federal charges that were just announced today. This Loughner guy has been charged with various charges related to murder and attempted murder of Federal officials, and there may be some difficulty getting a conviction in the case if Loughner's defense team can successfully claim that the shootings were completely random and he had no idea who his victims were.
In order to bolster their case, the Feds need to present sufficient evidence (in the form of written documents, e-mails, etc.) that Loughner targeted his victims (especially the Congresswoman) because of the Federal positions they held.
Someone has already removed the shrine in the backyard.