Here is a recipe for an action for Photoshop. I know you specifically states that you don't have access to Photoshop, but it might be useful to know the method anyway.
We assume that:
- All your images are flattened (only consists of a Background Layer).
- The images have different width and height.
- The top part which you want to keep (in blue) is always 50 px tall.
- The middle part which you want to cut out (in red) is always 90 px tall.
Method
We start out with an image like this:

Open the Actions panel, create a new Set, create a new Action within that set and start recording.
Perform Image > Canvas Size and set it up like this:

Make sure Relative is unticked. Set the Height field to 50 px and don't touch the Width field. Set the Anchor to center top.
This will crop away everything except for the top part, which you want to keep:

Perform Select > All and Edit > Copy to copy the top part of the image to the clipboard for later use.
Perform File > Revert to revert the image to its initial state:

Again perform Image > Canvas Size but this time with these settings:

Make sure Relative is ticked. Set the Height field to -90 px and leave the Width field at 0. Set the Anchor to center bottom.
This will crop away the top 90 px of the image:

Perform Edit > Paste to paste in the top part of the image we copied to the clipboard earlier:

The pasted content gets its own layer which is selected by default. Hold down Shift and left-click the Background layer to select that as well.
In the Options panel in the top, click the Align top edges button to align the top part with the top of the background:

Finally, perform Layer > Flatten Image to flatten the image and get the final result:

Running the action looks like this:
