One of the things you can do in anime versus on manga is to set the mood with music.
Anya's "Apparently, if you have love, you can fly" can be read as a silly joke in the manga - she just picked up those words from Becky earlier, and needed an excuse to give her 'art' to Damian. But the anime chose to not show Anya making a silly face while saying it - or at least, not as silly as in the manga - and more importantly the theme 'Small Daily Life' starts playing. The anime is saying - this is not a joke, Anya meant it.
This lovely theme notably played in two important scenes - when Anya thanked Twilight for adopting her from the orphanage and promised him she'd do her best at school at the end of Episode 5, and the scene where Anya remembers that moment, which segues into Loid and Yor discussing parenthood in Episode 7.
As I've written about these moments before - they depict people who don't really know how to vocalize their feelings showing love via their actions. For Anya, it's getting good grades for her papa, for Yor it's cooking for her brother, for Twilight it's deciding he needs to become a good father to his daughter.
This is probably the first time in the series where Anya understood why Damian is the way he is - in many ways, like herself, he just wants his father's love and approval. (This also explains her confession to him much later on about how she doesn't know whether Loid even likes her let along loves her, but she loves her papa with all her little heart... deep down, she knows Damian has similar doubts about where he fits within his family.)
So, there we go. The griffin isn't just an olive branch. It is not part of Anya's grand Friendship Scheme. This is her showing empathy towards the little boy who's just like her. It comes from the heart.