ということ is used to summarize something in your own words, especially something that someone else has said.
Maybe you’re having a birthday party and your friend is late. They’re making excuses about getting you a gift, and they’ll be there in an hour. You could say
私の誕生日を忘れたということですか。
“So what you’re saying is, you forgot my birthday?”
Breaking it down, という is quoting something, and こと is your general experience with something. In English, we would say it a bit backwards.
“The general thing” こと “that you are saying” という “is …”
といってもいい can be used to summarize something that you’ve said, telling your audience the gist of what you meant to say.
Your friend finally arrives at your party, two hours late. Your friend’s gift for you is a promotional item for your favorite anime, but that item went on sale just today. They hoped to arrive at the party on time, but the lines for this special gift were longer than they expected. They could finish their explanation
このプレゼントはとても人気だといってもいい。
“You could say this gift is really popular.”
Again, と is the quotation particle, but いう is in the て form. Specifically, it’s using the grammar for てもいい, “it would be fine.” A direct translation above might be
" ‘This gift is really popular.’ Saying that would be fine, or good, or correct."
The nuance would be that it was much more popular than your friend expected, and that popularity is the reason why they were so late.