Note:
The solution uses a browser addon (for Firefox only) to block said exit intent popup (Overlay Popup, to be precise).
The addon works perfectly well on website (received from the comments).
The solution uses images under instructions. Enable images in your browser if they are disabled via Preferences or an addon.
There are two addons that can achieve the goal (individually) with pros and cons mentioned below.
Description from Developer
YesScript lets you make a blacklist of sites that aren't allowed to run JavaScript. Use YesScript on sites that annoy you or hog your system resources. One click to the icon in the status bar turns scripts on or off for the current site.
The icon looks like
.
How to use YesScript?
Whenever you reach a website which uses such Overlay Popup,
- Click the YesScript icon
once to activate the addon. The icon of the addon will look like
, once activated.
- Reload the website using reload icon in Firefox, or by pressing Ctrl + R, or Fn+F5 (Fn is subjected to Laptops only).
- You can click the icon again to deactivate the addon on the website.
Pros
One-click solution to disable/enable the popup.
Cons
Possibly will break the functionality of the website since all the javascripts will be blocked.
Precisely because of the Cons of the last addon, I prefer the following addon with better control on the elements of the webpage.
Description from Developer
Yarip allows users to modify Web pages in a number of different ways. It works by injecting and applying user created code-snippets onto a Web page in order to change the look and feel and by using rule-based matching in order to remove elements (DOM) and block or redirect content (URLs).
This addon is usable from the context menu. Right-click anywhere on any website,

and the relevant entry in the menu will look like

How to use "Yet Another Remove It Permanently"?
Load the website and let the popup appear.

Right-click on any part of the popup (I did on red colored section) and move the cursor (highlight) on Yarip to open its sub-menu.

Go to DIV and choose Blacklist element. (Note that there can be more than one DIV entries under Yarip and the one to choose is mostly the last said entry.)

A windows will appear having details like

The details under Xpath may vary on other websites and Page will definitely vary on another website. Anyhow, click OK.
Reload the website using reload icon in Firefox, or by pressing Ctrl + R, or Fn+F5 (Fn is subjected to Laptops only).
Move the cursor towards Status bar or close tab icon and a transparent popup may come up like

Repeat step 2 and 3, and following image will show up. (Note that some websites will not need steps after step 7. This seems to be a different case.)

Click OK and repeat step 6. The popup won't appear again.
How to manage "Yet Another Remove It Permanently"?
Right-click anywhere on the website, highlight Yarip and select Manage Pages

A window will appear like (Note that black colored section will not be there -- other website entries, hence privacy issue)

The controls are obvious to use by now. Anyhow, if you choose to deactivate this addon on a website, choose the website entry in the left panel, go to bottom of the same panel and click Remove pages. You can remove individual DIV or other entries using the options at the bottom below right panel. Highlight and click desired option.
Pros
Absolutely wonderful addon. Gives fine grained control on the elements and allows you tinker with them.
Saves the settings so that in future (if you visit website again), you don't have to repeat the steps to hide the popup.
Works on most of the websites. (Worked on everyone I tried so far.)
Doesn't breaks functionality (if used wisely) of the website unlike aforementioned addon.
Cons
- Can be bit tricky to use for a newbie but nothing substantial I noticed.
Status: Objective Completed. Done!
Note that there are extensions for Google Chrome available to achieve the objective but they don't save the settings, and thus, resets whenever the page is refreshed. Let me know via comments if you find anything useful for Chrome