tilgen
to repay
To pay back a debt or a loan completely through installment payments or other payments.
Er hat hart gearbeitet, um sein Studiendarlehen innerhalb von fünf Jahren zu tilgen.
He worked hard to repay his student loan within five years.

to repay / erase
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to repay
To pay back a debt or a loan completely through installment payments or other payments.
Er hat hart gearbeitet, um sein Studiendarlehen innerhalb von fünf Jahren zu tilgen.
He worked hard to repay his student loan within five years.

'Tilgen' (to repay/to erase) is a formal word that you mainly find in written language, official documents, or an elevated style. It is used less often in everyday conversation.
Der Vertrag legt fest, wie die Restschuld zu tilgen ist.
The contract specifies how the remaining debt is to be repaid.
The difference between the meanings becomes clear through the object. If it is about money, e.g. 'Schulden' (debts) or 'Kredit' (loan), 'tilgen' means to repay. If it is about information, e.g. 'Daten' (data) or 'Eintrag' (entry), it means to delete.
Sie konnte den Kredit schneller tilgen als erwartet.
She was able to repay the loan faster than expected.
In a financial context, 'tilgen' (to repay) is almost always combined with words for monetary debts. Typical examples are: 'Schulden tilgen' (to repay debts), 'einen Kredit tilgen' (to repay a loan), or 'ein Darlehen tilgen' (to repay a loan).
Mit dem neuen Job kann er seine Schulden endlich tilgen.
With the new job, he can finally repay his debts.
In the meaning 'löschen' (to delete), 'tilgen' (to erase) is often used for abstract or digital things. Common combinations are: 'Daten tilgen' (to erase data), 'einen Eintrag tilgen' (to erase an entry), 'Spuren tilgen' (to erase traces), or also 'eine Erinnerung tilgen' (to erase a memory).
Er versuchte, die schmerzhafte Erinnerung aus seinem Gedächtnis zu tilgen.
He tried to erase the painful memory from his mind.
to remove
'entfernen' and 'tilgen' can both mean that something is no longer there or no longer visible. 'entfernen' is the normal, general word for many things: you can remove dirt, mistakes, or objects. 'tilgen' sounds stronger and often more formal. It fits especially with texts, data, or memories when something is meant to be completely deleted or wiped out. In everyday language, 'entfernen' is usually more natural. Use 'tilgen' when the disappearance is meant to sound especially final.

Der Techniker tilgt die alten Kundendaten aus dem System.
The technician erases the old customer data from the system.
Bitte entfernen Sie morgen die falsche Nummer aus der Liste.
Please remove the wrong number from the list tomorrow.