In current version, we use the following code to remove a possible \par at the end of each cell:
\tl_reverse:N \l__tblr_trim_temp_tl
\__tblr_remove_head_par:N \l__tblr_trim_temp_tl
\tl_reverse:N \l__tblr_trim_temp_tl
The code is cumbersome. To improve it we can append \l__tblr_quark to cell text, and apply
\tl_remove_once:Nn \l__tblr_cell_text_tl {\par\l__tblr_quark}