When I paste text from a PDF into indesign it creates a border which I cannot work out how to remove

Could be a pre-existing setting you accidentally turned on. InDesign can be sneaky here if you make changes with nothing selected they can become the default for new objects, and if you make changes with no documents open they can become defaults for future documents.

A few things worth checking:

First - from the PDF try selecting the Text and the use Right Click to bring up the contextual menu, then select Copy Formatted Text - sometimes helps

Somethings it might be

Paragraph Shading / Paragraph Borders
Select some of the text and look in the Paragraph panel menu for Paragraph Shading and Paragraph Borders. OCR'd PDF text can sometimes bring across unexpected formatting.

Paragraph Rules (Above/Below)
Check whether a Paragraph Rule is being applied. A thick rule spanning the text frame can sometimes look like a border.

Tables
PDF copy/paste occasionally creates tables without it being obvious. Click inside the text and press Esc to switch between text and cell selection. If table formatting is present you'll usually spot it immediately. I doubt it’s this for some reasons.

Text Frame Stroke
Draw a completely new text frame with the Type Tool and compare it. If new text frames also have a border, the default text frame stroke may have been changed. With nothing selected, set Stroke to None and try again.

Object Styles
Open the Object Styles panel and see whether the imported frames have an object style applied that's adding a stroke or other frame appearance.

Paragraph Styles
Check whether the text is using a paragraph style that includes Paragraph Borders/Shading.

Also inspect Basic Paragraph. If Basic Paragraph has been modified, those settings can cascade into other styles. A search for "Beware Basic Paragraph" will explain why many InDesign users avoid editing it.

Frame Edges vs Actual Borders
One other question does the border appear in PDF export or when printed? If it only appears on screen, it may simply be text frame edges (View > Extras > Hide Frame Edges), which are non-printing guides rather than actual borders.

A screenshot would probably identify the cause in a few seconds.

I think I have experienced this before but just tried to recreate it and wasn’t able to. Make sure to double check styles for everything (paragraph, character, object, table, etc.) just to rule out that there isn’t a hidden stroke somewhere in there. I think somehow when I would paste from a PDF it changed the default “basic text frame” style to have a stroke. 

Hi ​@Paul234752824r12,

Sorry to hear you’re running into this issue. Could you please confirm the exact InDesign version and OS details you’re currently using?

I tested this on InDesign 21.4 on Windows 11 using a sample OCR PDF on my end, but I was unable to reproduce the border behavior after autoflow. Could you please share a screenshot of the InDesign window showing the affected text frames and visible borders for better reference, as requested by the expert?

Additionally, please share a sample OCR PDF used for testing if possible. If the file is confidential, feel free to share it via DM using any public cloud-sharing platform such as Google Drive, Dropbox, WeTransfer, etc.

Looking forward to your update.

Thanks,
Abhishek

Screenshots might help.