I package the indesign file and export into PDF to the printer but they came back mentioning a few files has embed color profile. Does that mean I need to make sure every image in indesign has embed color profile unchecked before I can package and export to PDF again? The images are edited in photoshop before I work on indesign to make sure pictures are in CMYK but didn't realise it has embed color profile ticked.
If you are providing a PDF, you can Export to either the PDF/X-4 or PDF/X1a presets with the Output tab Destination set to Document CMYK, which will force all color into the document’s assigned CMYK space, and will not include Profiles.
Also, as general workflow strategy, you don’t have to make CMYK conversions in Photoshop— it’s more efficient to place RGB images with embedded profiles, and make the conversion to a CMYK profile via the Export Output tab.