Delaware Expungement of Criminal Records. Criminal History Background Check. (All Counties) is a process that allows individuals to have their criminal records sealed or destroyed. This allows for the individual to have their past criminal history removed from their public record. Expungement can be a helpful tool for individuals looking to start fresh and remove any obstacles that their criminal history may cause. Types of Delaware Expungement of Criminal Records. Criminal History Background Check. (All Counties) include: 1. Expungement of a Misdemeanor: This is the process of having a misdemeanor erased from a criminal record. 2. Expungement of DUI/DWI: This is the process of having a DUI or DWI erased from a criminal record. 3. Expungement of Arrests: This is the process of having an arrest erased from a criminal record. 4. Expungement of Felony: This is the process of having a felony erased from a criminal record. 5. Expungement of Minor Offenses: This is the process of having minor offenses erased from a criminal record.