kim, you stupid girl

Make your gif as you normally would, sharpen, colour, etc. Then we can get right into it.

First thing you gotta do is Duplicate your video layer/video group depending on your colouring style. (If you keep your colouring layers in a separate folder, make sure both clips are underneath it.)

Now that we have two videos, we'll leave the bottom one alone and add the blurring filter onto our duplicate from Filter -> Blur -> Gaussian Blur:

It's a personal choice how strong you want the blur to be, I usually go with anywhere between 3-5, depending on the quality of the footage and the size of the area I want to blur out.

And if you've done everything correctly, you should see something like this:

And this is where the magic happens. We add a Layer Mask to our duplicate as so:

Then, clicking onto the mask itself, using a black Paint Bucket tool we make the whole thing invisible, then using a white Brush tool we draw on the text to make the blur layer visible only in that area and nowhere else. (Make sure to set your brush's hardness to 0%, keeping the opacity on 100%.)

After you covered the whole text area, your Layer Mask should be looking something like this:

Also note that you can just use the Marquee (Selection) tool and a white Paint Bucket for similar results and quicker editing, I just personally prefer the way it looks with the brush.

Now, here is the trickier part. If you have a gif with multiple credits popping up at different times and you don't wanna keep the blur there when there is nothing underneath, you gotta toggle the ends and beginnings of the duplicate — in this case, duplicates.

Just repeat the same steps for all the separate parts you need to cover up and make sure you have different duplicate videos for all of them. Then adjust the ends of the clips on your Timeline according to where they need to be visible.

And ta-da! Your gif is all done and there are no pesky credits in sight.