Minor thing: Since 立つ is an intransitive verb, you can't say 「噂を立つ」. You have to say 「噂を立てる」, so it should be 「あの噂を立てたこと…」.
This sounds a little strange in Japanese (the wording is too literally translated from English), but it's almost grammatically correct. When a verb modifies a noun, there's no need for a connecting の between the verb and the noun. So it should just be 「覚えるタスク」.