Why did Elizabeth I think it necessary to keep Lady Mary Gray and her husband imprisoned?

[Me.]

2. Wasn't Elizabeth

“The great-granddaughter of Henry VII through his younger daughter, Mary, Jane was a first cousin once removed of Edward VI. In May 1553, she was married to Lord Guildford Dudley, a younger son of Edward's chief minister, John Dudley, Duke of Northumberland. In June 1553, Edward VI wrote his will, nominating Jane and her male heirs as successors to the Crown in part because his half-sister Mary was Roman Catholic while Jane was Protestant and would support the reformed Church of England, whose foundation Edward claimed to have laid. The will named his half-sisters Mary and Elizabeth illegitimate and removed them from succession. This step subverted their claims under the Third Succession Act.

After Edward's death, Jane was proclaimed queen on 10 July 1553 and awaited coronation in the Tower of London. Support for Mary grew very quickly and most of Jane's supporters abandoned her. The Privy Council decided to change sides and proclaimed Mary as queen on 19 July 1553, deposing Lady Jane. Her primary supporter, the Duke of Northumberland, was accused of treason and executed less than a month later. Jane was held as a prisoner at the Tower and was convicted of high treason in November 1553, which carried a sentence of death, though Mary initially spared her life. After her father, Henry Grey, 1st Duke of Suffolk, became part of Wyatt's rebellion of January and February 1554 against Queen Mary's intention to marry Philip of Spain, Jane was viewed as a threat to the crown; both Jane and her husband were executed”

https://en.wikipedia.org/wiki/Lady_Jane_Grey