The burning bushes could be moved if you really want to save them, and they're not too big for you to handle. They are quite inexpensive to buy, however, and you could simply let whoever is digging up the yard remove them for you at their expense and effort, then replace them if you choose. They can be invasive non-natives, though - birds eat the seeds and spread them quickly, and they sprout quite easily. You'll have to decide for yourself if it's worth your time and energy to move and replant them, or if it's easier to let them be removed and plant new ones, or to plant different shrubs altogether. There are many alternatives to burning bush if you choose to go with natives or non-invasive non-natives, depending on the soil and exposure where you'd want to plant them.

I hope this helps!

Laurel