Block builders today have full control of the content in their blocks and have the ability to remove and/or insert transactions at any position. You can find some more details on how searchers and builders interact, and a some criteria to look for in a block builder, in our Documentation and in Searching Post-Merge.
We are working on reducing these trust assumptions, since March we’ve been running a block builder inside an SGX enclave, bringing us one step closer toward transaction confidentiality and decentralization of the block-building role.
Moving forward, with SUAVE, we seek to substitute these trust guarantees further with robust cryptographic and cryptoeconomic assurances for comprehensive programmable privacy.