Noura, I'm not a toy expert but I would definitely recommend trimming any frayed edges off. A budgie can get its head, feet, or nails caught in it and trimming them may help prevent this.
Here is a thread about toys that also may help you: http://talkbudgies.com/budgie-product-reviews/64279-dangerous-toy-list-11.html
Here is a thread about toys that also may help you: http://talkbudgies.com/budgie-product-reviews/64279-dangerous-toy-list-11.html