It's possible that the issue is related to the conversion from Excel 2003 to 2007, but there are a few things you can try to remove the plot lines between two points on a line chart:

1. Double-click on the line chart to open the Chart Tools tab.
2. Click on the Design tab.
3. Click on the Select Data button.
4. In the Select Data Source dialog box, click on the Edit button under Legend Entries (Series).
5. In the Edit Series dialog box, click on the Line Color drop-down menu and select No Line.
6. Click OK to close all of the dialog boxes.

If this doesn't work, you can try selecting the data series in the chart and pressing the Delete key to remove the entire series. Then, re-enter the data and create a new chart without the plot lines.

Another option is to right-click on the plot line you want to remove and select Format Data Series. In the Format Data Series dialog box, click on the Line Style tab and select No Line. Click OK to close the dialog box.

If none of these options work, it's possible that the issue is related to the conversion from Excel 2003 to 2007. You may want to try opening the file in Excel 2003 and removing the plot lines before saving and reopening in Excel 2007.