To cut a very long story short and to put it way too simplistically, Lady Jane Grey was a threat to Mary I as long as she lived because she could be used as a figurehead for rebellion. Although Wyatt's Revolt had actually aimed to replace Mary with Elizabeth, Lady Jane Grey's father was involved in it and it was his actions which highlighted the need for Jane to "go". Mary was under pressure from the Spanish to deal with this threat and she did. It was not something she relished doing.
You can read more about Lady Jane Grey's fall at
https://www.theanneboleynfiles.com/the-execution-of-lady-jane-grey-part-one/4289/
http://www.elizabethfiles.com/lady-jane-grey-proclaimed-queen/3934/
http://www.elizabethfiles.com/sir-thomas-wyatt-the-younger/3793/
http://www.elizabethfiles.com/lady-jane-grey-facts/3575/
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So sad. Someone so young being executed merely for the actions of others rebelling on her behalf. I cant imagine Mary relished that decision. I dont think anyone would. But it makes sense. Execute one so that Mary wasnt obligated to execute thousands for rebelling.
Yes, Mary was very reluctant about having to have her cousin Lady Jane Grey executed. Although they had completely opposite religious views (Mary was a devote catholic, Jane a protestant reformer) they used to be on reasonably friendly terms in earlier years. Although Jane never wanted to be Queen, and in fact had said the crown should go to Mary, Mary sadly realised that Jane would always be a focal point for any attempts against her reign and rebellion and civil war was not what the country needed.