No worries! I don't have anything super specific in mind... It's a whole lot of things to be honest, I'm afraid if you wanted to seriously address this and make sure perception of the platform improved in this regard, you'd have to consider a big reworking of the communication. As it is now, the major selling points seem to be that it's easy to create complex animations, thanks to the features and the ability to create timelines that you can then manipulate easily. But in my own experience (and I don't claim it to be any more than that), complex animations (like a logo animation or a character doing a little dance or whatever) is a tiny percentage of what I'm using GSAP for; I'm more interested in moving around parts of the web page, adapting to user inputs on the fly, creating interactive content etc.
I guess on a more easy-to-implement level you could make sure to present TweenLite as not only the fundamental atom of animations, but also the default way to leverage GSAP's power for any kind of operation. The front page doesn't have a lot of things to really convey what GSAP can do; there's the video that goes too fast to really understand anything beyond "this is a powerhouse", then a list of plugins that don't really mean anything to you the first time you see them. If you go to https://greensock.com/gsap you'll see an animated banner (which furthers the impression that you will only use GSAP for static, self-contained animations) and then paragraphs saying that it's fast, robust and compatible – that are convincing, but don't work to expand your understanding of what the platform can do.
I'd say the best thing would be to try to get the user to see clear, impressive examples as soon as possible. If you go on https://threejs.org/ or http://animejs.com/, there's almost no words, they let the examples speak for themselves; it makes for pages that are maybe a bit too intimidating or obscure, but are very good at giving you a sense of what these tools are for and what they can do. Having a simpler, more friendly homepage for GSAP that immediately shows embedded examples (not just gifs or videos) of a big variety of uses, from the most basic tweens to more unconventional uses like delayedCall() and SVG manipulation and ScrollTo plugin, etc., would go a long way towards saying "look, you can basically create a movie with this, but also you can use it in tons of creative and web-specific ways".
I don't know for sure – I'm thinking the latter. Every time you explicitly perform an action on a tween or it restarts, it would recalculate. The use case is, say I want an animation of a frog jumping every X seconds towards the cursor; right now I'd probably have to call a function that creates a timeline with passed arguments. But I think it'd be nice to be able to create the timeline beforehand, and have a parameters to let it know that the direction of the jump should be reevaluated every time it runs.
(To be clear, I know this is doable now – what isn't with GSAP? – but I think it would be more intuitive and faster to have a parameter of its own inside the TweenLite and TimelineLite vars.)