Gaze-based applications are increasingly advancing with the availability of large datasets but ensuring data quality presents a substantial challenge when collecting data at scale. It further requires different parties to collaborate, therefore, privacy concerns arise. We propose QualitEye--the first method for verifying image-based gaze data quality. QualitEye employs a new semantic representation of eye images that contains the information required for verification while excluding irrelevant information for better domain adaptation. QualitEye covers a public setting where parties can freely exchange data and a privacy-preserving setting where parties cannot reveal their raw data nor derive gaze features/labels of others with adapted private set intersection protocols. We evaluate QualitEye on the MPIIFaceGaze and GazeCapture datasets and achieve a high verification performance (with a small overhead in runtime for privacy-preserving versions). Hence, QualitEye paves the way for new gaze analysis methods at the intersection of machine learning, human-computer interaction, and cryptography.