How can I completely remove brackets from citations in text?

All the time?  Just Edit the style Citation template to remove them.  (Edit>Output Styles>edit “your chosen output style”.  Remember if it is an installed style, to save it to a new name and to switch your manuscript to use the edited style. 

Only some of the time?  – the only way is to remove them from the template as above - and include them around your citations manually, when you want them there.