Version:

The Anvil is a simple 4x4 Crafting Table with the same options.
NOTE: Due to an old bug with ModTweaker, Anvil recipes are flipped diagonally (e.g., the dirt in the recipe below would be at the bottom left corner). This can be fixed by using the ShapedFixed versions - addShapedFixed and removeShapedFixed.

Shaped

Addition

mods.betterwithmods.Anvil.addShaped(IItemStack output, IIngredient[][] inputs);

mods.betterwithmods.Anvil.addShaped(<minecraft:dirt>, [
   [<minecraft:stone>, <minecraft:stone>, <minecraft:stone>, <minecraft:dirt>],
   [<minecraft:stone>, <minecraft:stone>, <minecraft:stone>, <minecraft:stone>],
   [<minecraft:stone>, <minecraft:stone>, <minecraft:stone>, <minecraft:stone>],
   [<minecraft:stone>, <minecraft:stone>, <minecraft:stone>, <minecraft:stone>]
]); // dirt is actually at bottom left in-game

Removal

mods.betterwithmods.Anvil.removeShaped(IItemStack output, @Optional IIngredient[][] inputs);

mods.betterwithmods.Anvil.removeShaped(<minecraft:dirt>);

mods.betterwithmods.Anvil.removeShaped(<minecraft:dirt>,[
   [<minecraft:stone>, <minecraft:stone>, <minecraft:stone>, <minecraft:dirt>],
   [<minecraft:stone>, <minecraft:stone>, <minecraft:stone>, <minecraft:stone>],
   [<minecraft:stone>, <minecraft:stone>, <minecraft:stone>, <minecraft:stone>],
   [<minecraft:stone>, <minecraft:stone>, <minecraft:stone>, <minecraft:stone>]
]); // dirt would actually be at bottom left in-game

Addition (Fixed)

mods.betterwithmods.Anvil.addShapedFixed(IItemStack output, IIngredient[][] inputs);

mods.betterwithmods.Anvil.addShapedFixed(<minecraft:dirt>, [
   [<minecraft:stone>, <minecraft:stone>, <minecraft:stone>, <minecraft:dirt>],
   [<minecraft:stone>, <minecraft:stone>, <minecraft:stone>, <minecraft:stone>],
   [<minecraft:stone>, <minecraft:stone>, <minecraft:stone>, <minecraft:stone>],
   [<minecraft:stone>, <minecraft:stone>, <minecraft:stone>, <minecraft:stone>]
]); // dirt is like the recipe says, at top right in-game

Removal (Fixed)

mods.betterwithmods.Anvil.removeShapedFixed(IItemStack output, @Optional IIngredient[][] inputs);

mods.betterwithmods.Anvil.removeShapedFixed(<minecraft:dirt>);

mods.betterwithmods.Anvil.removeShapedFixed(<minecraft:dirt>,[
   [<minecraft:stone>, <minecraft:stone>, <minecraft:stone>, <minecraft:dirt>],
   [<minecraft:stone>, <minecraft:stone>, <minecraft:stone>, <minecraft:stone>],
   [<minecraft:stone>, <minecraft:stone>, <minecraft:stone>, <minecraft:stone>],
   [<minecraft:stone>, <minecraft:stone>, <minecraft:stone>, <minecraft:stone>]
]); // dirt would be like the recipe says, at top right in-game

Shapeless

Addition

mods.betterwithmods.Anvil.addShapeless(IItemStack output, IIngredient[] inputs);

mods.betterwithmods.Anvil.addShapeless(<minecraft:dirt>, [
<minecraft:dirt>, <minecraft:dirt>, <minecraft:dirt>, <minecraft:dirt>,
<minecraft:dirt>, <minecraft:dirt>, <minecraft:dirt>, <minecraft:dirt>,
<minecraft:dirt>, <minecraft:dirt>, <minecraft:dirt>, <minecraft:dirt>,
<minecraft:dirt>, <minecraft:dirt>, <minecraft:dirt>, <minecraft:dirt>
]);

Removal

mods.betterwithmods.Anvil.removeShapeless(IItemStack output, @Optional IIngredient[] inputs);

mods.betterwithmods.Anvil.removeShapeless(<minecraft:dirt>);

mods.betterwithmods.Anvil.removeShapeless(<minecraft:dirt>, [
<minecraft:dirt>, <minecraft:dirt>, <minecraft:dirt>, <minecraft:dirt>,
<minecraft:dirt>, <minecraft:dirt>, <minecraft:dirt>, <minecraft:dirt>,
<minecraft:dirt>, <minecraft:dirt>, <minecraft:dirt>, <minecraft:dirt>,
<minecraft:dirt>, <minecraft:dirt>, <minecraft:dirt>, <minecraft:dirt>
]);

Clearing

You can clear all the recipes from the Anvil by using the following:

mods.betterwithmods.Anvil.removeAll();