"I have seen this anime."
Well... sort of. Depends on the context.
Regular past tense (-た or -ました) is generally used when there's an implication of a specific point in time. Ex: if you're talking with someone about what you did last week and you said 「映画を見た」, it would be understood that you were talking about watching a movie last week.
On the other hand, sometimes you need to express that you did something in the past without implying a certain time period. That's what -たことがあります does. It's basically saying "at some point in my life, could be days or years ago, I did this thing." Or, more succinctly, "I have experienced doing this thing."
You'll also often hear this as a question (-たことがありますか？), which translates to "Have you ever...?" A very useful phrase to phrase to remember!
ah so basically it's the present perfect! I was wondering if Jpnese makes a distinction between the simple past and the present perfect.
Both are correct, but by using は instead of を, you are singling out "this anime" as the topic. So there are other anime out there that you have not seen, but you have seen THIS anime. The usage can get pretty complicated., but that's the gist.
I switched the は and the が and got marked wrong. Is the business about tagging the topic the reason why?
は can replace を and が everywhere (if there's not a は already). が cannot replace anything.