As mentioned in issue 76 at the BH repo, its new version creates compilation issues with package TDA. I have not had time to really dive into this, but this may be caused by TDA also including some Boost headers to that we may get a conflict between different versions. The container library is included in BH so you could skip that; dealing with serialization may be trickier but an update to the current version may help.
Please reach out if you have any questions, and a big Thank You! for maintaining TDA on CRAN.