Final answer:
William the Conqueror (option A) was the contender with a formidable military reputation and claimed the English throne in 1066, based on an alleged pledge of fealty from Harold Godwinson.
Step-by-step explanation:
The strong contender for the English throne in 1066, known for his formidable military reputation and a legitimate claim that he based on an alleged agreement with the previous king, was William the Conqueror (A). This claim stemmed from a feudal pledge of fealty that Harold Godwinson, a powerful Anglo-Saxon noble and later King of England, had reportedly made to William of Normandy.
According to William, Harold had pledged fealty to him, which William used to justify his invasion of England, though Harold denied having done so. In the famed Battle of Hastings, depicted in the monumental Bayeux Tapestry, William defeated Harold and became the first Norman King of England, a pivotal moment that deeply influenced the subsequent history of England.