The ToS have the answers to all your questions in this case, but you will need to check yourself on the artist’s gig.
If said illustrator’s gig page contains any text regarding usage rights, or has any sort of commercial licence Gig Extra or package option which you have bought along with/in the order, all possible lifetime rights to the art you have received from the delivered order (checked as complete) have already been transferred to you. You can only lose them if you decide to cancel an order before it’s done or after its completion; the rights will return to the seller in that case. And when we talk all possible rights we mean personal, licensing (as in leasing it rather than selling/completely giving it away) and commercial use. You own it forever and you can publish it, edit it, destroy it, etc.
Example from a random seller’s gig, in this case it’s inside the basic package and not even a Gig Extra at the bottom of the page to pay more money for:
Only if you have purchased a lesser package without commercial rights, you may not publish nor edit the artwork. If you have bought a gig without rights (meaning you are only entitled to personal use), you may need to discuss things with the artist and wait for them.
My biggest concern here would be to hire someone who can Photoshop letters or text nicely to make it look like it was never modified, with any edits blending in the background efficiently, if you really can’t reach or find them elsewhere. I assume you’ve bought something with commercial use already since you plan on publishing a book.