Can I remove bullet points from a whole table?

the bullets are a default text setting in my tables.

Hi Matt:

InDesign defaults are set two ways: either in an open document with nothing selected (a document default) or with no documents open (a system default). This will is be a continuing problem until you reset the default for this document, or for all future documents. Click in a table cell to see what is controlling the formatting in the Paragraph styles panel. Then fix it there forever.

~Barb

you need to set up paragraph styles, you will drive yourself mad without them.

choose all cells in a table - open paragraph panel - open menu of panel - bullets and numbering - list type: None - ok

But who's say to you to work without paragraph styles? Next time define all needed styles and work fast without some manual operations!