How to perform an action when a specific string is removed from a list of strings?

You could handle it in the place you remove it.

 if (GUI.Button(new Rect(100, 75, 135, 20), i1)) 
 { 
     pHealth += 10;
     Inventory.Remove(Inventory[0]); 
 }

If the Inventory is being changed from other places, you need to wrap the List in a class that fire events when you add or remove stuff.

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 
 public class Example : MonoBehaviour
 {
     // Instead of using List<string>, we use InventoryList
     InventoryList list = new InventoryList();
 
     void Start()
     {
         // register event handlers
         list.onValueAdded += (sender, value) => print("Added " + value);
         list.onValueRemoved += (sender, value) => print("Removed " + value);
         list.onValueChanged += (sender, index) => print("Changed list[" + index + "] " + sender[index]);

         // use the list
         list.Add("Pasta");
         list.Add("Dog");
         list.Add("Student");
         list.Remove("Student Loan"); // won't be logged because it doesnt exist.
         list[1] = "Creepy Dog";
         list.Remove("Creepy Dog");

         // Dump some data so we can see what happened
         print("List is now accurate. Let's review its contents");    
         foreach (var item in list)
         {
             print("Item: " + item);
         }
     }
 }

Let's pause and look at the output before we look at InventoryList.

 public class InventoryList : IEnumerable<string>
 {
     private List<string> list = new List<string>();
 
     public delegate void ValueEvent(InventoryList list, string value);
     public delegate void ValueChangedEvent(InventoryList list, int index);
 
     public event ValueEvent onValueAdded;
     public event ValueEvent onValueRemoved;
     public event ValueChangedEvent onValueChanged;
 
     public InventoryList() { }
 
     public InventoryList(IEnumerable<string> source)
     {
         list = new List<string>(source);
     }
 
     public void Add(string value)
     {
         list.Add(value);
         if (onValueAdded != null)
             onValueAdded(this, value);
     }
 
     public bool Remove(string value)
     {
         bool removed = list.Remove(value);
         if (removed && onValueRemoved != null)
             onValueRemoved(this, value);
         return removed;
     }
 
     public IEnumerator<string> GetEnumerator()
     {
         return ((IEnumerable<string>)list).GetEnumerator();
     }
 
     IEnumerator IEnumerable.GetEnumerator()
     {
         return ((IEnumerable<string>)list).GetEnumerator();
     }
 
     public string this[int index]
     {
         get { return list[index]; }
         set
         {
             if (list[index] != value)
             {
                 list[index] = value;
                 onValueChanged(this, index);
             }
         }
     }
 }