See Rakas v. Illinois, 439 U.S. 128, 134 (1978) (internal citations removed):
A person who is aggrieved by an illegal search and seizure only
through the introduction of damaging evidence secured by a
search of a third person's premises or property has not had
any of his Fourth Amendment rights infringed. And since the exclusionary rule is an attempt to effectuate the guarantees of the Fourth Amendment, it is proper to permit only defendants whose Fourth Amendment rights have been violated to benefit from the rule's protections. ... Even if such a person is not a defendant in the action, he may be able to recover damages for the violation of his Fourth Amendment rights, or seek redress under state law for invasion of privacy or trespass.
And at 140:
Analyzed in these terms, the question is whether the challenged search and seizure violated the Fourth Amendment
rights of a criminal defendant who seeks to exclude the evidence obtained during it. That inquiry in turn requires a
determination of whether the disputed search and seizure has
infringed an interest of the defendant which the Fourth
Amendment was designed to protect.
Thus, the only person who would be able to seek exclusion of the evidence is the defendant against whom the evidence would be introduced (Alice, in your scenario). However, I think you have intentionally written this so that Alice's Fourth Amendment rights were not infringed, so she would not be able to argue for exclusion. I think you recognize this.
Steve's remedy is to "recover damages for the violation of his Fourth Amendment rights, or seek redress under state law for invasion of privacy or trespass."