Tea tree maintenance
When some of the flower branches appear to have died, how should they be removed
Certified GKH Gardening Expert
Tough question without photos or description of size of plant and size of branches.
General information is; confirm branch is dead by scraping off a small piece of the bark an looking for a green growing layer. If so, water or wait for rains and anticipate new growth in spring. If dry and brown and small twigs snap off when bent, then consider that branch as dead. Cut back to the juncture at the parent stem. Use a sharp pruning shears, or a pruning saw.
If the plant is large and/or the amount of dying/dead branches is excessive, best to hire a professional who can make appropriate decisions on selective pruning.
Have you had one inch of rain yet in Sonoma? If not and if it's not irrigated, I advise deep watering to rescue your tea tree from drought stress. And deep water once a month during the long dry season next year. Tea tree is drought tolerent, to an extent, but not immune to severe water deficit. Water and fertilize with a complete organic fertilizer like Dr Earth or Down To Earth brands, all purpose.