How to stop phony device checking pop-ups on iPad?

The majority of threats to which you will be invariably exposed will surface via web pages or embedded links within email. These browser-based attacks can largely be mitigated by installing a good Content and Ad-blocking product. One of the very best and most respected within the Apple App Store - designed for iPad, iPhone and Mac - is 1Blocker for Safari.

https://apps.apple.com/gb/app/1blocker-for-safari/id1365531024

1Blocker is highly configurable - and crucially does not rely upon an external proxy-service of dubious provenance. All processing takes place on your device - and contrary to expectations, Safari will run faster and more efficiently. 

Unwanted content is not simply filtered after download (a technique used by basic/inferior products), but instead undesirable embedded content blocked form download.  1Blocker has also introduced its new “Firewall” functions - that are explicitly designed to block “trackers”. Being implemented at the network-layer, this additional protection works across all Apps.

A further measure to improve protection is to use a security focussed DNS Service in preference to automatic DNS settings. This can either be set on a per-device basis in Settings, or can be set-up on your home Router - and in so doing extends the benefit of this specific protection to other devices on your local network. I strongly recommend using one of the following DNS services - for which IPv4 and IPv6 server addresses are listed:

Quad9 (recommended)

9.9.9.9

149.112.112.112

2620:fe::fe

2620:fe::9

OpenDNS

208.67.222.222

208.67.220.220

2620:0:ccc::2

2620:0:ccd::2

Cloudflare+APNIC

1.1.1.1

1.0.0.1

2606:4700:4700::1111

2606:4700:4700::1001

Use of the above DNS services will help to shield you from “known bad” websites and URLs - and when used alongside 1Blocker, or other Content Blocker provides defense in depth.

DNSecure, a free third-party App, can simply configuration of secure DNS settings on you iPad and iPhone - enabling access to DNS services using encrypted DoH and DoT protocols:

https://apps.apple.com/app/dnsecure/id1533413232

There's a couple of settings you can adjust! Give these a try:

Clear browser data.

These pop-ups are often triggered by stored cookies or scripts that re-open the same malicious ad chain.

Safari

• • Settings → Safari
  • Tap Clear History and Website Data

Chrome

• • Open Chrome → … → Settings
  • Privacy → Clear Browsing Data
  • Select:
    • Cookies
    • Cached images/files

Firefox

• • Menu → Settings → Data Management
  • Clear all website data

Block pop-ups and fraudulent sites

Safari (important even if you mainly use Chrome/Firefox)

• • Settings → Safari
  • Enable:
    • Block Pop-ups
    • Fraudulent Website Warning

Remove notification permissions

Some sites trick you into allowing notifications that later push fake alerts.

• • Settings → Notifications
  • Scroll through apps/browsers
  • Look for anything suspicious or unfamiliar
  • Turn OFF notifications for browsers if needed

Also check:

• • Settings → Safari → Notifications (if present)
  • In Chrome/Firefox → Site settings → Notifications

Download an ad blocker

Tons of options but two great ones:

• • 1Blocker
  • AdGuard

You're very welcome. Am always delighted to share useful help and guidance.

The basic 1Blocker App (free) allows you to select a single blocking category, whereas the full version (for a modest and very worthwhile subscription) allows selection of multiple blocking categories and adds the "firewall" functionality (at the network layer) providing additional protection for other Apps. 1Blocker actually creates a blocking ruleset that is applied to Safari - the browser App actually performing the processing. Perhaps counterintuitive, but with blocking rulesets applied, Safari runs faster and more efficiently; unwanted content simply isn't loaded.

Consider also using DNSecure, as listed within my initial reply, choosing Quad9 as the DNS provider. DNSecure provides an additional and complementary protection mechanism. Sites with know bad content are simply sink-holed.

Those are ads that the website you are visiting is paid to show to you. If your browser has a Pop-Up Blocker setting, you can try that, otherwise you will need an AdBlocker to eliminate most of them. The other option is to let the Website Administrator know that you don't like those fraudulent advertisements. They may not care since they are getting paid for them, but Feedback is always a good idea and if they understand that users will go elsewhere, they may listen.