Remover um item valioso era um sinal de que ele sabia seu destino. Ele sabe que será executado agora ou podemos dizer queimado vivo.
A partir de IGN
When Varys heard a door open and the footsteps of soldiers approaching, that was the sign that his time had come to an end, so he decided to burn the letter he was writing to destroy the evidence of his plan and then prepare himself for death by removing his finery.
Removing one’s valuables before imminent demise is a gesture we’ve seen in other stories before. It’s sort of a ritual of accepting one’s death, a way to prepare for what’s to come.
O mesmo artigo também cobre as teorias dos fãs, um dos populares é o anel de veneno deixado por Tyrion ou outra pessoa para terminar o trabalho.
A mesma teoria do veneno é coberta por gamespot também e vá mais fundo:
Zooming in on Varys's rings and brightening up the image doesn't reveal any conspicuous blue crystals. In fact, the ring we get the best look at seems to have represented Varys's loyalty to the Targaryen queen--it appears to be this ring from jewelry retailer Mey's official partnership with the show. The retailer calls it an "allegiance ring," and their site claims that Varys, Tyrion, Jorah, and Grey Worm have all worn one since Season 7. It was designed to look like a dragon spine. In taking it off, Varys is symbolically shedding the symbol of his loyalty to Daenerys.
But Varys is still loyal to Jon, who he now knows is also a Targaryen. Even though we didn't see the obvious blue poison crystal as Varys removed all his rings, the show seemed to focus on their removal just long enough that it might be important in the finale.
Após SO8E06:
poison ring theory has been debunked by the absence of that plot in later episodes so it seems it was only allegiance ring and he removed as he was going to die.