Should I cut the dead flowers off my tellima grandiflora?

Hi Bloomsbury, and welcome to GOY :)
I've not known mine to repeat flower after cutting off the flower spikes, so I think it only flowers the once. Lovely leaf shape though, so you can still enjoy it for it's foliage.

If you let it go to seed, you will have plants all over the garden - it is very prolific

i have had a second odd flower in september but not a decent show. but as andrewr says they self seed all over but a few extras are nice. welcome to GoY too.