As Henry VIII's only survivign child, no one had a stronger claim than Elizabeth. The only way Mary's (or any Stuart's) claim could be stronger was if one considered Elizabeth illegitimate. Catholics did consider Elizabeth illegitimate because they did not recognize Henry's divorce and remarriage. But by the laws of the time, after Henry had "protestantized" the country, she was legitimate.
“Catholics did consider Elizabeth illegitimate “
That was almost all of Europe!
That’s why I said “arguably”. Henry married Anne Boleyn and begat Elizabeth while Katharine was still alive. Most of Europe considered that to be adultery, as Elizabeth very well knew.
“As Henry VIII’s only survivign child, no one had a stronger claim than Elizabeth.”
That might be true - if she were not illegitimate. Elizabeth had plotted to gain the throne - with the aid of Thomas Seymour (the second husband of Catherine Parr who was the widow of Henry VIII) since at least 1549. Seymour was executed for this. Elizabeth refused to admit her guilt but was known to be guilty. As the daughter of a king, and having admitted no wrong doing, she was not tried or publicly punished.