It only seems to appear when I have set up alternative strokes on the columns or rows. If I delete a row or column at the end with alternative fills applied it looks fine with no strange line. It happens everytime I use tables in Indesign, has done since I can remember. When I look at the table styles it just has the default basic table setup. I'm using CS3.
Here is a test file, you can see when I have deleted either a row or column at the end it has created a thick black line.
http://www.filefactory.com/file/ofo2057txgv/n/Table_Test_indd
I've got the file, but I'm not sure what you are trying to show me. It's a single frame with a blank table. The table has a 1 point stroke applied as the right and bottom border.
In order to help you I'm going to need to see the file the table that is giving you a problem. I'll need to have it as you want it it to appear so that I can try to delete a row and see what happens. It does no good if you've already deleted the row and not reset the strokes.
Okay here is the table that I am actually trying to edit and delete rows and columns. I have left it without deleting anything so you can see if the lines appear when you delete the last row or column.
Thanks
http://www.filefactory.com/file/4uzdl4ia2gzx/n/Table_Test_indd_zip
While you would do well to actually set up a custom set of cellstyles and a table style for this, I was able to solve the problem in your file by going to Window > Type and Tables > Table Styles, then selecting the [Basic Table] style, right clicking and choosing Edit [Basic Table]. Under Table Setup change the Table Border specifications so the stroke type is explicitly set to None. For some reason setting the weight to 0 is not sufficient here.
Checked you file and when we delete the row at the bottom the table border get added at the bottom ,
Select your table ,
Go to Table-->Table options-->Table Setup
In the dialog box , You will have a option under "Table border" :- "Weight" , which would be blank, enter "0 pt" in it and Click "OK"
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