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The budwood likely will work. I'd try rather than throw it out. Sometimes a second bud will emerge.
Did it take a while for them to push? What did you do to encourage growth? I budded some about a month ago and just took a blade and made a few notches above the bud. Should I prune back the rootstock? First time budding citrus so looking for some tips (I know there have been other posts and online sources about this but looking for a technique that someone with recent success vouches for 😀)