Which of the following rights does not pertain to the mineral estate?

The right to lease property to third parties is not a characteristic of the mineral estate. The mineral estate typically refers to the rights associated with the extraction and ownership of minerals beneath the surface of a property, such as oil, gas, coal, and other minerals.

When considering the other rights listed, the right to receive delay rental is relevant because it pertains to payments made by a lessee to delay drilling operations, reflecting the lessor's rights to compensation while the lessee holds the lease. Similarly, the right to receive bonus refers to the upfront payment made when a lease is signed, another key aspect of the mineral rights. The right to execute an oil and gas lease involves granting permission for the extraction of oil and gas, which falls squarely within the scope of mineral rights.

Leasing property to third parties generally applies more to the surface estate, where landowners may choose to sublease or rent their property without necessarily involving the mineral rights or the extraction of resources. Thus, this particular right is distinctly separate from the rights inherent to the mineral estate, making it the correct answer in this context.