Diagonalizable Thue equations: revisited

Let $$r,h\in {\mathbb {N}}$$ with $$r\ge 7$$ and let $$F(x,y)\in {Z}}[x ,y]$$ be a binary form such that $$\begin{aligned} F(x , y) =(\alpha x + \beta y)^r -(\gamma \delta y)^r, \end{aligned}$$ where $$\alpha $$ $$\beta $$\gamma $$\delta are algebraic constants -\beta \gamma \ne 0$$ . We establish upper bounds for the number of primitive solutions to Thue inequality $$0<|F(x, y)| \le h$$ improving an earlier result Siegel Akhtari, Saradha, Sharma.